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https://wiki.swarma.org/api.php?action=feedcontributions&feedformat=atom&user=TYcl20 集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 - 用户贡献 [zh-cn] 2026-11-04T10:00:40Z 用户贡献 MediaWiki 1.35.0 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33965 时间序列分析 2023-02-13T12:05:31Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ===分析方法===<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些模型中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ===面板数据===<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==='''分析'''===<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> <br /> 推测特定时间点的信息可通过以下方式完成：<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===时间序列分析在信号处理上的应用===<br /> {{see also|Signal processing|Estimation theory}}<br /> 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，该方法在二战期间迅速得以推广。数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯和其他学者完成了信号的滤波处理，且预测了在特定时间段中的信号值。相关知识可参见卡尔曼滤波器，参数估测和数字信号处理的介绍。<br /> ===时间序列的分割处理===<br /> {{main|Time-series segmentation}}<br /> <br /> <br /> 时间序列的分割处理是将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。时间序列分割的目标是识别时间序列中的分段临界点，并分析每个分段的动态特性。此外，时间序列可以建模成一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ===模型 ===<br /> <br /> <br /> 时间序列数据的模型可以用多种形式来表示不同的随机过程。在对过程层次的变化进行建模时，三大重要模型是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个模型线性地依赖于以前的数据点。这些模型的结合产生了自回归移动平均(ARMA)和模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对三大重要模型进行了推广。处理矢量值数据的模型的扩展可以在多元时间序列模型下继续完成，有一些是前面的首字母缩略词被扩展，例如一个初始的“ v”代表“矢量”； VAR 代表向量自回归模型。从这些模型的另外一组扩展可以发现观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应)；与多变量情况的区别在于这种强迫序列可能是在实验者的控制之下所得到的。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> <br /> <br /> 研究数据对过往的数据点的非线性依赖关系是有趣的，因为它有产生混沌时间序列的可能性。然而，更重要的是，使用来自非线性模型的预测优于来自线性模型的预测。例如非线性自回归外生模型的预测准确度优于线性的回顾模型。 <br /> <br /> <br /> 在其他的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型有ARCH模型，其中包括GARCH，TARCH，EGARCH，FIGARCH，CGARCH等模型。在这里，差异性的变化与观测到的过往值有关，或者是预测值。在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列能说明在多个尺度上的时间依赖。具体参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔可夫可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，它能将语音序列转换成文本。<br /> <br /> ===时间序列的表示方法===<br /> :<br /> <br /> 时间序列分析有许多不同的表示方法。一种表示指定时间序列 x 的通用方法是: x = (X1，X2，...)。<br /> <br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===时间序列的相关概念--平稳过程与遍历过程===<br /> 大部分的时间序列建立在两个条件之下: <br /> * 平稳过程<br /> * 遍历过程<br /> <br /> <br /> 时间序列的平稳性的概念必须考虑两个重要的概念: 严格平稳性和二阶平稳性。人们可以通过这2个概念去建立模型和开发应用程序。<br /> <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或处于非平稳状态下的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。<br /> <br /> ===形成，分析时间序列数据的工具与方法===<br /> 形成，分析时间序列数据的工具与方法包括:<br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数)<br /> * 调整互相关函数和自相关函数以去除慢分量的贡献<br /> * 在频域中执行一个傅里叶变换来调查这个序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图<br /> * <br /> * EWMA 图<br /> * 非趋势波动分析<br /> * 非线性混合效应建模<br /> * <br /> * 动态时间规整互相关<br /> * <br /> * 动态贝氏网路<br /> * 时频分析技术:<br /> * <br /> * 快速傅里叶变换连续小波转换<br /> * <br /> * 短时距傅里叶变换<br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析<br /> * <br /> * <br /> * 复发图<br /> * <br /> * 递归量化分析<br /> * <br /> * Lyapunov 指数<br /> * <br /> * <br /> * <br /> * <br /> <br /> ===时间序列量化分析的指标与准则===<br /> * 单变量线性测量<br /> * <br /> * 矩(数学)<br /> * <br /> * 谱带功率<br /> * <br /> * 谱边缘频率<br /> * <br /> * 累积能量(信号处理)<br /> * <br /> * 自相关函数特性<br /> * <br /> * Hjorth 参数<br /> * <br /> * FFT 参数<br /> * <br /> * 自回归模型参数<br /> * <br /> * 相关积分<br /> * 相关密度<br /> * 相关熵<br /> * 近似熵<br /> * 小波熵<br /> * 色散熵<br /> * 涨落色散熵<br /> * 高阶方法边际可预测动力学相似性<br /> * 指数状态空间相异性度量<br /> * 李亚普诺夫指数排列方法<br /> * <br /> * 本地流<br /> * 其他单变量度量<br /> * <br /> * 算法复杂度<br /> * <br /> * 柯氏复杂性估计<br /> * <br /> * 隐马尔可夫模型状态<br /> * <br /> * 粗糙路径签名<br /> * <br /> * 替代时间序列和替代校正<br /> * <br /> * 递归损失(非平稳度)<br /> * 双变量线性度量<br /> * <br /> * 最大线性互相关<br /> * <br /> * 线性相干性(信号处理)<br /> * 双变量非线性度量<br /> * <br /> * 非线性相互依赖<br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学)<br /> * <br /> * 相位同步的度量<br /> * <br /> * 相位锁定的度量<br /> * <br /> * 相似度量:<br /> * <br /> * 互相关<br /> * <br /> * <br /> * 动态时间规整<br /> * <br /> * <br /> * 隐马尔可夫模型<br /> * <br /> * <br /> * 编辑距离<br /> * <br /> * 总相关性<br /> * <br /> * Newey-West 估计<br /> * <br /> * Prais-Winsten 变换<br /> * <br /> * 数据作为向量在乌雷松度量化定理<br /> * <br /> * <br /> * 明氏距离<br /> * <br /> * 马氏距离<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差<br /> * <br /> * <br /> * 窗口标准差<br /> * <br /> * 数据解释为随机序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数<br /> * <br /> * 数据解释为概率分布函数<br /> * <br /> * Kolmogorov-Smirnov 检验<br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ===时间序列的可视化===<br /> <br /> <br /> 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> * <br /> <br /> === 重叠图 === <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> === 分离图 === <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ===相关资料===<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ===参考文献===<br /> *{{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> *[[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> *{{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> *{{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> *[[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]].<br /> *{{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer,<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> *[[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> *{{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> === 相关书籍 === <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社<br /> *<br /> <br /> ===外部链接===<br /> <br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33964 时间序列分析 2023-02-12T14:48:17Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ===分析方法===<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些模型中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ===面板数据===<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==='''分析'''===<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> <br /> 推测特定时间点的信息可通过以下方式完成：<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===时间序列分析在信号处理上的应用===<br /> {{see also|Signal processing|Estimation theory}}<br /> 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，该方法在二战期间迅速得以推广。数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯和其他学者完成了信号的滤波处理，且预测了在特定时间段中的信号值。相关知识可参见卡尔曼滤波器，参数估测和数字信号处理的介绍。<br /> ===时间序列的分割处理===<br /> {{main|Time-series segmentation}}<br /> <br /> <br /> 时间序列的分割处理是将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。时间序列分割的目标是识别时间序列中的分段临界点，并分析每个分段的动态特性。此外，时间序列可以建模成一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ===模型 ===<br /> <br /> <br /> 时间序列数据的模型可以用多种形式来表示不同的随机过程。在对过程层次的变化进行建模时，三大重要模型是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个模型线性地依赖于以前的数据点。这些模型的结合产生了自回归移动平均(ARMA)和模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对三大重要模型进行了推广。处理矢量值数据的模型的扩展可以在多元时间序列模型下继续完成，有一些是前面的首字母缩略词被扩展，例如一个初始的“ v”代表“矢量”； VAR 代表向量自回归模型。从这些模型的另外一组扩展可以发现观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应)；与多变量情况的区别在于这种强迫序列可能是在实验者的控制之下所得到的。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> <br /> <br /> 研究数据对过往的数据点的非线性依赖关系是有趣的，因为它有产生混沌时间序列的可能性。然而，更重要的是，使用来自非线性模型的预测优于来自线性模型的预测。例如非线性自回归外生模型的预测准确度优于线性的回顾模型。 <br /> <br /> <br /> 在其他的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型有ARCH模型，其中包括GARCH，TARCH，EGARCH，FIGARCH，CGARCH等模型。在这里，差异性的变化与观测到的过往值有关，或者是预测值。在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列能说明在多个尺度上的时间依赖。具体参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔可夫可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，它能将语音序列转换成文本。<br /> <br /> ===时间序列的表示方法===<br /> :<br /> <br /> 时间序列分析有许多不同的表示方法。一种表示指定时间序列 x 的通用方法是: x = (X1，X2，...)。<br /> <br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===时间序列的相关概念--平稳过程与遍历过程===<br /> 大部分的时间序列建立在两个条件之下: <br /> * 平稳过程<br /> * 遍历过程<br /> <br /> <br /> 时间序列的平稳性的概念必须考虑两个重要的概念: 严格平稳性和二阶平稳性。人们可以通过这2个概念去建立模型和开发应用程序。<br /> <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或处于非平稳状态下的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。<br /> <br /> ===形成，分析时间序列数据的工具与方法===<br /> 形成，分析时间序列数据的工具与方法包括:<br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数)<br /> * 调整互相关函数和自相关函数以去除慢分量的贡献<br /> * 在频域中执行一个傅里叶变换来调查这个序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图<br /> * <br /> * EWMA 图<br /> * 非趋势波动分析<br /> * 非线性混合效应建模<br /> * <br /> * 动态时间规整互相关<br /> * <br /> * 动态贝氏网路<br /> * 时频分析技术:<br /> * <br /> * 快速傅里叶变换连续小波转换<br /> * <br /> * 短时距傅里叶变换<br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析<br /> * <br /> * <br /> * 复发图<br /> * <br /> * 递归量化分析<br /> * <br /> * Lyapunov 指数<br /> * <br /> * <br /> * <br /> * <br /> <br /> ===时间序列量化分析的指标与准则===<br /> * 单变量线性测量<br /> * <br /> * 矩(数学)<br /> * <br /> * 谱带功率<br /> * <br /> * 谱边缘频率<br /> * <br /> * 累积能量(信号处理)<br /> * <br /> * 自相关函数特性<br /> * <br /> * Hjorth 参数<br /> * <br /> * FFT 参数<br /> * <br /> * 自回归模型参数<br /> * <br /> * 相关积分<br /> * 相关密度<br /> * 相关熵<br /> * 近似熵<br /> * 小波熵<br /> * 色散熵<br /> * 涨落色散熵<br /> * 高阶方法边际可预测动力学相似性<br /> * 指数状态空间相异性度量<br /> * 李亚普诺夫指数排列方法<br /> * <br /> * 本地流<br /> * 其他单变量度量<br /> * <br /> * 算法复杂度<br /> * <br /> * 柯氏复杂性估计<br /> * <br /> * 隐马尔可夫模型状态<br /> * <br /> * 粗糙路径签名<br /> * <br /> * 替代时间序列和替代校正<br /> * <br /> * 递归损失(非平稳度)<br /> * 双变量线性度量<br /> * <br /> * 最大线性互相关<br /> * <br /> * 线性相干性(信号处理)<br /> * 双变量非线性度量<br /> * <br /> * 非线性相互依赖<br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学)<br /> * <br /> * 相位同步的度量<br /> * <br /> * 相位锁定的度量<br /> * <br /> * 相似度量:<br /> * <br /> * 互相关<br /> * <br /> * <br /> * 动态时间规整<br /> * <br /> * <br /> * 隐马尔可夫模型<br /> * <br /> * <br /> * 编辑距离<br /> * <br /> * 总相关性<br /> * <br /> * Newey-West 估计<br /> * <br /> * Prais-Winsten 变换<br /> * <br /> * 数据作为向量在乌雷松度量化定理<br /> * <br /> * <br /> * 明氏距离<br /> * <br /> * 马氏距离<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差<br /> * <br /> * <br /> * 窗口标准差<br /> * <br /> * 数据解释为随机序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数<br /> * <br /> * 数据解释为概率分布函数<br /> * <br /> * Kolmogorov-Smirnov 检验<br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ===时间序列的可视化===<br /> <br /> <br /> 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> * <br /> <br /> === 重叠图 === <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> === 分离图 === <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ===相关资料===<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ===参考文献===<br /> *{{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> *[[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> *{{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> *{{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> *[[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]].<br /> *{{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer,<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> *[[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> *{{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> === 相关书籍 === <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社<br /> *<br /> <br /> ===外部链接===<br /> <br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> *参考文献<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33963 时间序列分析 2023-02-12T14:29:10Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ===分析方法===<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些模型中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ===面板数据===<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==='''分析'''===<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> <br /> 推测特定时间点的信息可通过以下方式完成：<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===时间序列分析在信号处理上的应用===<br /> {{see also|Signal processing|Estimation theory}}<br /> 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，该方法在二战期间迅速得以推广。数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯和其他学者完成了信号的滤波处理，且预测了在特定时间段中的信号值。相关知识可参见卡尔曼滤波器，参数估测和数字信号处理的介绍。<br /> ===时间序列的分割处理===<br /> {{main|Time-series segmentation}}<br /> <br /> <br /> 时间序列的分割处理是将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。时间序列分割的目标是识别时间序列中的分段临界点，并分析每个分段的动态特性。此外，时间序列可以建模成一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ===模型 ===<br /> <br /> <br /> 时间序列数据的模型可以用多种形式来表示不同的随机过程。在对过程层次的变化进行建模时，三大重要模型是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个模型线性地依赖于以前的数据点。这些模型的结合产生了自回归移动平均(ARMA)和模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对三大重要模型进行了推广。处理矢量值数据的模型的扩展可以在多元时间序列模型下继续完成，有一些是前面的首字母缩略词被扩展，例如一个初始的“ v”代表“矢量”； VAR 代表向量自回归模型。从这些模型的另外一组扩展可以发现观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应)；与多变量情况的区别在于这种强迫序列可能是在实验者的控制之下所得到的。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> <br /> <br /> 研究数据对过往的数据点的非线性依赖关系是有趣的，因为它有产生混沌时间序列的可能性。然而，更重要的是，使用来自非线性模型的预测优于来自线性模型的预测。例如非线性自回归外生模型的预测准确度优于线性的回顾模型。 <br /> <br /> <br /> 在其他的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型有ARCH模型，其中包括GARCH，TARCH，EGARCH，FIGARCH，CGARCH等模型。在这里，差异性的变化与观测到的过往值有关，或者是预测值。在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列能说明在多个尺度上的时间依赖。具体参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔可夫可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，它能将语音序列转换成文本。<br /> <br /> ===时间序列的表示方法===<br /> :<br /> <br /> 时间序列分析有许多不同的表示方法。一种表示指定时间序列 x 的通用方法是: x = (X1，X2，...)。<br /> <br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===时间序列的相关概念--平稳过程与遍历过程===<br /> 大部分的时间序列建立在两个条件之下: <br /> * 平稳过程<br /> * 遍历过程<br /> <br /> <br /> 时间序列的平稳性的概念必须考虑两个重要的概念: 严格平稳性和二阶平稳性。人们可以通过这2个概念去建立模型和开发应用程序。<br /> <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或处于非平稳状态下的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。<br /> <br /> ===形成，分析时间序列数据的工具与方法===<br /> 形成，分析时间序列数据的工具与方法包括:<br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数)<br /> * 调整互相关函数和自相关函数以去除慢分量的贡献<br /> * 在频域中执行一个傅里叶变换来调查这个序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图<br /> * <br /> * EWMA 图<br /> * 非趋势波动分析<br /> * 非线性混合效应建模<br /> * <br /> * 动态时间规整互相关<br /> * <br /> * 动态贝氏网路<br /> * 时频分析技术:<br /> * <br /> * 快速傅里叶变换连续小波转换<br /> * <br /> * 短时距傅里叶变换<br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析<br /> * <br /> * <br /> * 复发图<br /> * <br /> * 递归量化分析<br /> * <br /> * Lyapunov 指数<br /> * <br /> * <br /> * <br /> * <br /> <br /> ===时间序列量化分析的指标与准则===<br /> * 单变量线性测量<br /> * <br /> * 矩(数学)<br /> * <br /> * 谱带功率<br /> * <br /> * 谱边缘频率<br /> * <br /> * 累积能量(信号处理)<br /> * <br /> * 自相关函数特性<br /> * <br /> * Hjorth 参数<br /> * <br /> * FFT 参数<br /> * <br /> * 自回归模型参数<br /> * <br /> * 相关积分<br /> * 相关密度<br /> * 相关熵<br /> * 近似熵<br /> * 小波熵<br /> * 色散熵<br /> * 涨落色散熵<br /> * 高阶方法边际可预测动力学相似性<br /> * 指数状态空间相异性度量<br /> * 李亚普诺夫指数排列方法<br /> * <br /> * 本地流<br /> * 其他单变量度量<br /> * <br /> * 算法复杂度<br /> * <br /> * 柯氏复杂性估计<br /> * <br /> * 隐马尔可夫模型状态<br /> * <br /> * 粗糙路径签名<br /> * <br /> * 替代时间序列和替代校正<br /> * <br /> * 递归损失(非平稳度)<br /> * 双变量线性度量<br /> * <br /> * 最大线性互相关<br /> * <br /> * 线性相干性(信号处理)<br /> * 双变量非线性度量<br /> * <br /> * 非线性相互依赖<br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学)<br /> * <br /> * 相位同步的度量<br /> * <br /> * 相位锁定的度量<br /> * <br /> * 相似度量:<br /> * <br /> * 互相关<br /> * <br /> * <br /> * 动态时间规整<br /> * <br /> * <br /> * 隐马尔可夫模型<br /> * <br /> * <br /> * 编辑距离<br /> * <br /> * 总相关性<br /> * <br /> * Newey-West 估计<br /> * <br /> * Prais-Winsten 变换<br /> * <br /> * 数据作为向量在乌雷松度量化定理<br /> * <br /> * <br /> * 明氏距离<br /> * <br /> * 马氏距离<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差<br /> * <br /> * <br /> * 窗口标准差<br /> * <br /> * 数据解释为随机序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数<br /> * <br /> * 数据解释为概率分布函数<br /> * <br /> * Kolmogorov-Smirnov 检验<br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ===时间序列的可视化===<br /> <br /> <br /> 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> * <br /> <br /> === 重叠图 === <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> === 分离图 === <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ===相关资料===<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ===参考文献===<br /> *{{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> *[[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> *{{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> *{{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> *[[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]].<br /> *{{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer,<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> *[[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> *{{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> === 相关书籍 === <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社<br /> *<br /> <br /> ===外部链接===<br /> <br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33962 时间序列分析 2023-02-12T14:21:35Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ===分析方法===<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些模型中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ===面板数据===<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==='''分析'''===<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> <br /> 推测特定时间点的信息可通过以下方式完成：<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===时间序列分析在信号处理上的应用===<br /> {{see also|Signal processing|Estimation theory}}<br /> 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，该方法在二战期间迅速得以推广。数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯和其他学者完成了信号的滤波处理，且预测了在特定时间段中的信号值。相关知识可参见卡尔曼滤波器，参数估测和数字信号处理的介绍。<br /> ===时间序列的分割处理===<br /> {{main|Time-series segmentation}}<br /> <br /> <br /> 时间序列的分割处理是将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。时间序列分割的目标是识别时间序列中的分段临界点，并分析每个分段的动态特性。此外，时间序列可以建模成一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ===模型 ===<br /> <br /> <br /> 时间序列数据的模型可以用多种形式来表示不同的随机过程。在对过程层次的变化进行建模时，三大重要模型是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个模型线性地依赖于以前的数据点。这些模型的结合产生了自回归移动平均(ARMA)和模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对三大重要模型进行了推广。处理矢量值数据的模型的扩展可以在多元时间序列模型下继续完成，有一些是前面的首字母缩略词被扩展，例如一个初始的“ v”代表“矢量”； VAR 代表向量自回归模型。从这些模型的另外一组扩展可以发现观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应)；与多变量情况的区别在于这种强迫序列可能是在实验者的控制之下所得到的。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> <br /> <br /> 研究数据对过往的数据点的非线性依赖关系是有趣的，因为它有产生混沌时间序列的可能性。然而，更重要的是，使用来自非线性模型的预测优于来自线性模型的预测。例如非线性自回归外生模型的预测准确度优于线性的回顾模型。 <br /> <br /> <br /> 在其他的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型有ARCH模型，其中包括GARCH，TARCH，EGARCH，FIGARCH，CGARCH等模型。在这里，差异性的变化与观测到的过往值有关，或者是预测值。在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列能说明在多个尺度上的时间依赖。具体参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔可夫可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，它能将语音序列转换成文本。<br /> <br /> ===时间序列的表示方法===<br /> :<br /> <br /> 时间序列分析有许多不同的表示方法。一种表示指定时间序列 x 的通用方法是: x = (X1，X2，...)。<br /> <br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===时间序列的相关概念--平稳过程与遍历过程===<br /> 大部分的时间序列建立在两个条件之下: <br /> * 平稳过程<br /> * 遍历过程<br /> <br /> <br /> 时间序列的平稳性的概念必须考虑两个重要的概念: 严格平稳性和二阶平稳性。人们可以通过这2个概念去建立模型和开发应用程序。<br /> <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或处于非平稳状态下的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。<br /> <br /> ===形成，分析时间序列数据的工具与方法===<br /> 形成，分析时间序列数据的工具与方法包括:<br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数)<br /> * 调整互相关函数和自相关函数以去除慢分量的贡献<br /> * 在频域中执行一个傅里叶变换来调查这个序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图<br /> * <br /> * EWMA 图<br /> * 非趋势波动分析<br /> * 非线性混合效应建模<br /> * <br /> * 动态时间规整互相关<br /> * <br /> * 动态贝氏网路<br /> * 时频分析技术:<br /> * <br /> * 快速傅里叶变换连续小波转换<br /> * <br /> * 短时距傅里叶变换<br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析<br /> * <br /> * <br /> * 复发图<br /> * <br /> * 递归量化分析<br /> * <br /> * Lyapunov 指数<br /> * <br /> * <br /> * <br /> * <br /> <br /> ===时间序列量化分析的指标与准则===<br /> * 单变量线性测量<br /> * <br /> * 矩(数学)<br /> * <br /> * 谱带功率<br /> * <br /> * 谱边缘频率<br /> * <br /> * 累积能量(信号处理)<br /> * <br /> * 自相关函数特性<br /> * <br /> * Hjorth 参数<br /> * <br /> * FFT 参数<br /> * <br /> * 自回归模型参数<br /> * <br /> * 相关积分<br /> * 相关密度<br /> * 相关熵<br /> * 近似熵<br /> * 小波熵<br /> * 色散熵<br /> * 涨落色散熵<br /> * 高阶方法边际可预测动力学相似性<br /> * 指数状态空间相异性度量<br /> * 李亚普诺夫指数排列方法<br /> * <br /> * 本地流<br /> * 其他单变量度量<br /> * <br /> * 算法复杂度<br /> * <br /> * 柯氏复杂性估计<br /> * <br /> * 隐马尔可夫模型状态<br /> * <br /> * 粗糙路径签名<br /> * <br /> * 替代时间序列和替代校正<br /> * <br /> * 递归损失(非平稳度)<br /> * 双变量线性度量<br /> * <br /> * 最大线性互相关<br /> * <br /> * 线性相干性(信号处理)<br /> * 双变量非线性度量<br /> * <br /> * 非线性相互依赖<br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学)<br /> * <br /> * 相位同步的度量<br /> * <br /> * 相位锁定的度量<br /> * <br /> * 相似度量:<br /> * <br /> * 互相关<br /> * <br /> * <br /> * 动态时间规整<br /> * <br /> * <br /> * 隐马尔可夫模型<br /> * <br /> * <br /> * 编辑距离<br /> * <br /> * 总相关性<br /> * <br /> * Newey-West 估计<br /> * <br /> * Prais-Winsten 变换<br /> * <br /> * 数据作为向量在乌雷松度量化定理<br /> * <br /> * <br /> * 明氏距离<br /> * <br /> * 马氏距离<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差<br /> * <br /> * <br /> * 窗口标准差<br /> * <br /> * 数据解释为随机序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数<br /> * <br /> * 数据解释为概率分布函数<br /> * <br /> * Kolmogorov-Smirnov 检验<br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ===时间序列的可视化===<br /> <br /> <br /> 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> * <br /> <br /> = 重叠图 = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> = 分离图 = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ===相关资料===<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ===参考文献===<br /> {{Reflist|2}}<br /> <br /> *{{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> *[[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> *{{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> *{{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> *[[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]].<br /> *{{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer,<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> *[[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> *{{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> === 相关书籍 === <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社<br /> *<br /> <br /> ===外部链接===<br /> <br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33961 时间序列分析 2023-02-12T12:21:37Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ===分析方法===<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些模型中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ===面板数据===<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==='''分析'''===<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> <br /> 推测特定时间点的信息可通过以下方式完成：<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===时间序列分析在信号处理上的应用===<br /> {{see also|Signal processing|Estimation theory}}<br /> 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，该方法在二战期间迅速得以推广。数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯和其他学者完成了信号的滤波处理，且预测了在特定时间段中的信号值。相关知识可参见卡尔曼滤波器，参数估测和数字信号处理的介绍。<br /> ===时间序列的分割处理===<br /> {{main|Time-series segmentation}}<br /> <br /> <br /> 时间序列的分割处理是将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。时间序列分割的目标是识别时间序列中的分段临界点，并分析每个分段的动态特性。此外，时间序列可以建模成一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ===模型 ===<br /> <br /> <br /> 时间序列数据的模型可以用多种形式来表示不同的随机过程。在对过程层次的变化进行建模时，三大重要模型是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个模型线性地依赖于以前的数据点。这些模型的结合产生了自回归移动平均(ARMA)和模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对三大重要模型进行了推广。处理矢量值数据的模型的扩展可以在多元时间序列模型下继续完成，有一些是前面的首字母缩略词被扩展，例如一个初始的“ v”代表“矢量”； VAR 代表向量自回归模型。从这些模型的另外一组扩展可以发现观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应)；与多变量情况的区别在于这种强迫序列可能是在实验者的控制之下所得到的。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> <br /> <br /> 研究数据对过往的数据点的非线性依赖关系是有趣的，因为它有产生混沌时间序列的可能性。然而，更重要的是，使用来自非线性模型的预测优于来自线性模型的预测。例如非线性自回归外生模型的预测准确度优于线性的回顾模型。 <br /> <br /> <br /> 在其他的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型有ARCH模型，其中包括GARCH，TARCH，EGARCH，FIGARCH，CGARCH等模型。在这里，差异性的变化与观测到的过往值有关，或者是预测值。在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列能说明在多个尺度上的时间依赖。具体参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔可夫可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，它能将语音序列转换成文本。<br /> <br /> ===时间序列的表示方法===<br /> :<br /> <br /> 时间序列分析有许多不同的表示方法。一种表示指定时间序列 x 的通用方法是: x = (X1，X2，...)。<br /> <br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===时间序列的相关概念--平稳过程与遍历过程===<br /> 大部分的时间序列建立在两个条件之下: <br /> * 平稳过程<br /> * 遍历过程<br /> <br /> <br /> 时间序列的平稳性的概念必须考虑两个重要的概念: 严格平稳性和二阶平稳性。人们可以通过这2个概念去建立模型和开发应用程序。<br /> <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或处于非平稳状态下的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。<br /> <br /> ===形成，分析时间序列数据的工具与方法===<br /> 形成，分析时间序列数据的工具与方法包括:<br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数)<br /> * 调整互相关函数和自相关函数以去除慢分量的贡献<br /> * 在频域中执行一个傅里叶变换来调查这个序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图<br /> * <br /> * EWMA 图<br /> * 非趋势波动分析<br /> * 非线性混合效应建模<br /> * <br /> * 动态时间规整互相关<br /> * <br /> * 动态贝氏网路<br /> * 时频分析技术:<br /> * <br /> * 快速傅里叶变换连续小波转换<br /> * <br /> * 短时距傅里叶变换<br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析<br /> * <br /> * <br /> * 复发图<br /> * <br /> * 递归量化分析<br /> * <br /> * Lyapunov 指数<br /> * <br /> * <br /> * <br /> * <br /> <br /> ===时间序列量化分析的指标与准则===<br /> * 单变量线性测量<br /> * <br /> * 矩(数学)<br /> * <br /> * 谱带功率<br /> * <br /> * 谱边缘频率<br /> * <br /> * 累积能量(信号处理)<br /> * <br /> * 自相关函数特性<br /> * <br /> * Hjorth 参数<br /> * <br /> * FFT 参数<br /> * <br /> * 自回归模型参数<br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流<br /> * 其他单变量度量<br /> * <br /> * 算法复杂度<br /> * <br /> * 柯氏复杂性估计<br /> * <br /> * 隐马尔可夫模型状态<br /> * <br /> * 粗糙路径签名<br /> * <br /> * 替代时间序列和替代校正<br /> * <br /> * 递归损失(非平稳度)<br /> * 双变量线性度量<br /> * <br /> * 最大线性互相关<br /> * <br /> * 线性相干性(信号处理)<br /> * 双变量非线性度量<br /> * <br /> * 非线性相互依赖<br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学)<br /> * <br /> * 相位同步的度量<br /> * <br /> * 相位锁定的度量<br /> * <br /> * 相似度量:<br /> * <br /> * 互相关<br /> * <br /> * <br /> * 动态时间规整<br /> * <br /> * <br /> * 隐马尔可夫模型<br /> * <br /> * <br /> * 编辑距离<br /> * <br /> * 总相关性<br /> * <br /> * Newey-West 估计<br /> * <br /> * Prais-Winsten 变换<br /> * <br /> * 数据作为向量在乌雷松度量化定理<br /> * <br /> * <br /> * 明氏距离<br /> * <br /> * 马氏距离<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差<br /> * <br /> * <br /> * 窗口标准差<br /> * <br /> * 数据解释为随机序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数<br /> * <br /> * 数据解释为概率分布函数<br /> * <br /> * Kolmogorov-Smirnov 检验<br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ===时间序列的可视化===<br /> <br /> <br /> 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> * <br /> <br /> = 重叠图 = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> = 分离图 = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ===相关资料===<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ===参考文献===<br /> {{Reflist|2}}<br /> <br /> *{{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> *[[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> *{{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> *{{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> *[[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]].<br /> *{{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer,<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> *[[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> *{{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> === 相关书籍 === <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社<br /> *<br /> <br /> ===外部链接===<br /> <br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33960 时间序列分析 2023-02-11T14:49:27Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数值Numeric数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ===分析方法===<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些模型中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ===面板数据===<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==='''分析'''===<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> <br /> 推测特定时间点的信息可通过以下方式完成：<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===时间序列分析在信号处理上的应用===<br /> {{see also|Signal processing|Estimation theory}}<br /> 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，该方法在二战期间迅速得以推广。数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯和其他学者完成了信号的滤波处理，且预测了在特定时间段中的信号值。相关知识参见卡尔曼滤波器，参数估测和数字信号处理的介绍。<br /> ===时间序列的分割处理===<br /> {{main|Time-series segmentation}}<br /> <br /> <br /> 时间序列的分割处理是将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。时间序列分割的目标是识别时间序列中的分段临界点，并分析每个分段的动态特性。此外，时间序列可以建模成一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ===模型 ===<br /> <br /> <br /> 时间序列数据的模型可以用多种形式来表示不同的随机过程。在对过程层次的变化进行建模时，三大重要模型是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个模型线性地依赖于以前的数据点。这些模型的结合产生了自回归移动平均(ARMA)和模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对三大重要模型进行了推广。处理矢量值数据的模型的扩展可以在多元时间序列模型下继续完成，有一些是前面的首字母缩略词被扩展，例如一个初始的“ v”代表“矢量”； VAR 代表向量自回归模型。从这些模型的另外一组扩展可以发现观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应)；与多变量情况的区别在于这种强迫序列可能是在实验者的控制之下所得到的。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> <br /> 研究数据对过往的数据点的非线性依赖关系是有趣的，主要是它有产生混沌时间序列的可能性。然而，更重要的是，使用来自非线性模型的预测优于来自线性模型的预测。例如非线性自回归外生模型的预测准确度优于线性的回顾模型。 <br /> <br /> <br /> 在其他的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型有ARCH模型，其中包括GARCH，TARCH，EGARCH，FIGARCH，CGARCH等模型。在这里，差异性的变化与观测到的过往值有关，或者是预测值。在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列能说明在多个尺度上的时间依赖。具体参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> A [[Hidden Markov model]] (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest [[dynamic Bayesian network]]. HMM models are widely used in [[speech recognition]], for translating a time series of spoken words into text.<br /> <br /> A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.<br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔科姆可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，用于将语音序列转换成文本。<br /> <br /> ===Notation===<br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series ''X'' that is indexed by the [[natural number]]s is written<br /> :''X'' = (''X''<sub>1</sub>, ''X''<sub>2</sub>, ...).<br /> <br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written<br /> :X = (X1, X2, ...).<br /> <br /> = = = 表示法 = = 用于时间序列分析的许多不同的表示法。一个用于指定时间序列 x 的通用符号是: x = (X1，X2，...)。<br /> <br /> Another common notation is<br /> :''Y'' = (''Y<sub>t</sub>'': ''t'' ∈ ''T''),<br /> where ''T'' is the [[index set]].<br /> <br /> Another common notation is<br /> :Y = (Yt: t ∈ T),<br /> where T is the index set.<br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===Conditions===<br /> There are two sets of conditions under which much of the theory is built:<br /> * [[Stationary process]]<br /> * [[Ergodic process]]<br /> <br /> There are two sets of conditions under which much of the theory is built:<br /> * Stationary process<br /> * Ergodic process<br /> <br /> 这个理论的大部分建立在两个条件之下: <br /> * 平稳过程遍历过程<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: [[strict stationarity]] and [[Stationary process#Weaker forms of stationarity|second-order stationarity]]. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: strict stationarity and second-order stationarity. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> 然而，平稳性的概念必须扩展到考虑两个重要的概念: 严格平稳性和二阶平稳性。模型和应用程序都可以在这些条件中的每一种情况下开发，尽管后一种情况下的模型可能被认为只是部分具体说明。<br /> <br /> In addition, time-series analysis can be applied where the series are [[Cyclostationary process|seasonally stationary]] or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in [[time-frequency analysis]] which makes use of a [[time–frequency representation]] of a time-series or signal.<ref>Boashash, B. (ed.), (2003) ''Time-Frequency Signal Analysis and Processing: A Comprehensive Reference'', Elsevier Science, Oxford, 2003 {{isbn|0-08-044335-4}}</ref><br /> <br /> In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.Boashash, B. (ed.), (2003) Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003 <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或非平稳的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。波阿什，b。我不知道你在说什么。) ，(2003)《时频信号分析与处理: 综合参考》，爱思唯尔科学出版社，牛津，2003<br /> <br /> ===形成，分析时间序列数据的工具与方法===<br /> 形成，分析时间序列数据的工具与方法包括:<br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数)<br /> * 调整互相关函数和自相关函数以去除慢分量的贡献<br /> * 在频域中执行一个傅里叶变换来调查这个序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图<br /> * <br /> * EWMA 图<br /> * 非趋势波动分析<br /> * 非线性混合效应建模<br /> * <br /> * 动态时间规整互相关<br /> * <br /> * 动态贝氏网路<br /> * 时频分析技术:<br /> * <br /> * 快速傅里叶变换连续小波转换<br /> * <br /> * 短时距傅里叶变换<br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析<br /> * <br /> * <br /> * 复发图<br /> * <br /> * 递归量化分析<br /> * <br /> * Lyapunov 指数<br /> * <br /> * <br /> * <br /> * <br /> <br /> ===时间序列量化分析的指标与准则===<br /> * 单变量线性测量<br /> * <br /> * 矩(数学)<br /> * <br /> * 谱带功率<br /> * <br /> * 谱边缘频率<br /> * <br /> * 累积能量(信号处理)<br /> * <br /> * 自相关函数特性<br /> * <br /> * Hjorth 参数<br /> * <br /> * FFT 参数<br /> * <br /> * 自回归模型参数<br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流<br /> * 其他单变量度量<br /> * <br /> * 算法复杂度<br /> * <br /> * 柯氏复杂性估计<br /> * <br /> * 隐马尔可夫模型状态<br /> * <br /> * 粗糙路径签名[1] Chevyrev，i. ，Kormilitzin，a。(2016)“ a Primer on the Signature Method in Machine Learning，arXiv: 1603.03788 v1”<br /> * <br /> * 替代时间序列和替代校正<br /> * <br /> * 递归损失(非平稳度)<br /> * 双变量线性度量<br /> * <br /> * 最大线性互相关<br /> * <br /> * 线性相干性(信号处理)<br /> * 双变量非线性度量<br /> * <br /> * 非线性相互依赖<br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学)<br /> * <br /> * 相位同步的度量<br /> * <br /> * 相位锁定的度量<br /> * <br /> * 相似度量:<br /> * <br /> * 互相关<br /> * <br /> * <br /> * 动态时间规整<br /> * <br /> * <br /> * 隐马尔可夫模型<br /> * <br /> * <br /> * 编辑距离<br /> * <br /> * 总相关性<br /> * <br /> * Newey-West 估计<br /> * <br /> * Prais-Winsten 变换<br /> * <br /> * 数据作为向量在乌雷松度量化定理<br /> * <br /> * <br /> * 明氏距离<br /> * <br /> * 马氏距离<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差<br /> * <br /> * <br /> * 窗口标准差<br /> * <br /> * 数据解释为随机序列<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数<br /> * <br /> * 数据解释为概率分布函数<br /> * <br /> * Kolmogorov-Smirnov 检验<br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ==Visualization==<br /> <br /> <br /> = = 可视化 = = 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> ===Overlapping charts===<br /> * [[Braided graphs]]<br /> * Line charts<br /> * Slope graphs<br /> * {{iw2|GapChart||fr}}<br /> <br /> * Braided graphs<br /> * Line charts<br /> * Slope graphs<br /> * <br /> <br /> = = = = 重叠图 = = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> ===Separated charts===<br /> * [[Horizon graphs]]<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> * Horizon graphs<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> = = = = = 分离图表 = = = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ==See also==<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ==References==<br /> {{Reflist|2}}<br /> <br /> ==Further reading==<br /> * {{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> * [[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> * {{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> * {{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> * [[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]]. {{ISBN|978-0-12-564901-8}}<br /> * {{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer, {{ISBN|978-3-319-52451-1}}<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> * [[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> * {{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> = = 进一步阅读 = = <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社。<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社。<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去。北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社。<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社。<br /> *<br /> <br /> ==External links==<br /> {{Commons category}}<br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> <br /> *Introduction to Time series Analysis (Engineering Statistics Handbook) — A practical guide to Time series analysis.<br /> <br /> = = 外部链接 = = <br /> * 时间序列分析导论(工程统计手册)ー时间序列分析实用指南。<br /> <br /> {{Statistics}}<br /> {{Portal bar|Mathematics}}<br /> {{Authority control}}<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> <br /> <br /> <br /> Category:Statistical data types<br /> Category:Mathematical and quantitative methods (economics)<br /> Category:Machine learning<br /> <br /> 类别: 统计数据类型类别: 数学和定量方法(经济学)类别: 机器学习<br /> <br /> <noinclude><br /> <br /> <small>This page was moved from [[wikipedia:en:Time series]]. Its edit history can be viewed at [[时间序列分析/edithistory]]</small></noinclude><br /> <br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33959 时间序列分析 2023-02-11T14:43:38Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数值Numeric数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ===分析方法===<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些模型中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ===面板数据===<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==='''分析'''===<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> <br /> 推测特定时间点的信息可通过以下方式完成：<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===时间序列分析在信号处理上的应用===<br /> {{see also|Signal processing|Estimation theory}}<br /> 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，该方法在二战期间迅速得以推广。数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯和其他学者完成了信号的滤波处理，且预测了在特定时间段中的信号值。相关知识参见卡尔曼滤波器，参数估测和数字信号处理的介绍。<br /> ===时间序列的分割处理===<br /> {{main|Time-series segmentation}}<br /> <br /> <br /> 时间序列的分割处理是将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。时间序列分割的目标是识别时间序列中的分段临界点，并分析每个分段的动态特性。此外，时间序列可以建模成一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ===模型 ===<br /> <br /> <br /> 时间序列数据的模型可以用多种形式来表示不同的随机过程。在对过程层次的变化进行建模时，三大重要模型是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个模型线性地依赖于以前的数据点。这些模型的结合产生了自回归移动平均(ARMA)和模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对三大重要模型进行了推广。处理矢量值数据的模型的扩展可以在多元时间序列模型下继续完成，有一些是前面的首字母缩略词被扩展，例如一个初始的“ v”代表“矢量”； VAR 代表向量自回归模型。从这些模型的另外一组扩展可以发现观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应)；与多变量情况的区别在于这种强迫序列可能是在实验者的控制之下所得到的。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> <br /> 研究数据对过往的数据点的非线性依赖关系是有趣的，主要是它有产生混沌时间序列的可能性。然而，更重要的是，使用来自非线性模型的预测优于来自线性模型的预测。例如非线性自回归外生模型的预测准确度优于线性的回顾模型。 <br /> <br /> <br /> 在其他的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型有ARCH模型，其中包括GARCH，TARCH，EGARCH，FIGARCH，CGARCH等模型。在这里，差异性的变化与观测到的过往值有关，或者是预测值。在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列能说明在多个尺度上的时间依赖。具体参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> A [[Hidden Markov model]] (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest [[dynamic Bayesian network]]. HMM models are widely used in [[speech recognition]], for translating a time series of spoken words into text.<br /> <br /> A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.<br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔科姆可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，用于将语音序列转换成文本。<br /> <br /> ===Notation===<br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series ''X'' that is indexed by the [[natural number]]s is written<br /> :''X'' = (''X''<sub>1</sub>, ''X''<sub>2</sub>, ...).<br /> <br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written<br /> :X = (X1, X2, ...).<br /> <br /> = = = 表示法 = = 用于时间序列分析的许多不同的表示法。一个用于指定时间序列 x 的通用符号是: x = (X1，X2，...)。<br /> <br /> Another common notation is<br /> :''Y'' = (''Y<sub>t</sub>'': ''t'' ∈ ''T''),<br /> where ''T'' is the [[index set]].<br /> <br /> Another common notation is<br /> :Y = (Yt: t ∈ T),<br /> where T is the index set.<br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===Conditions===<br /> There are two sets of conditions under which much of the theory is built:<br /> * [[Stationary process]]<br /> * [[Ergodic process]]<br /> <br /> There are two sets of conditions under which much of the theory is built:<br /> * Stationary process<br /> * Ergodic process<br /> <br /> 这个理论的大部分建立在两个条件之下: <br /> * 平稳过程遍历过程<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: [[strict stationarity]] and [[Stationary process#Weaker forms of stationarity|second-order stationarity]]. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: strict stationarity and second-order stationarity. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> 然而，平稳性的概念必须扩展到考虑两个重要的概念: 严格平稳性和二阶平稳性。模型和应用程序都可以在这些条件中的每一种情况下开发，尽管后一种情况下的模型可能被认为只是部分具体说明。<br /> <br /> In addition, time-series analysis can be applied where the series are [[Cyclostationary process|seasonally stationary]] or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in [[time-frequency analysis]] which makes use of a [[time–frequency representation]] of a time-series or signal.<ref>Boashash, B. (ed.), (2003) ''Time-Frequency Signal Analysis and Processing: A Comprehensive Reference'', Elsevier Science, Oxford, 2003 {{isbn|0-08-044335-4}}</ref><br /> <br /> In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.Boashash, B. (ed.), (2003) Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003 <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或非平稳的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。波阿什，b。我不知道你在说什么。) ，(2003)《时频信号分析与处理: 综合参考》，爱思唯尔科学出版社，牛津，2003<br /> <br /> ===Tools===<br /> Tools for investigating time-series data include:<br /> <br /> Tools for investigating time-series data include:<br /> <br /> = = = 调查时间序列数据的工具包括:<br /> <br /> * Consideration of the [[autocorrelation|autocorrelation function]] and the [[Spectral density|spectral density function]] (also [[cross-correlation function]]s and cross-spectral density functions)<br /> * [[Scaled correlation|Scaled]] cross- and auto-correlation functions to remove contributions of slow components<ref name="Nikolicetal">{{cite journal |last1=Nikolić |first1=D. |last2=Muresan |first2=R. C. |last3=Feng |first3=W. |last4=Singer |first4=W. |year=2012 |title=Scaled correlation analysis: a better way to compute a cross-correlogram |journal=European Journal of Neuroscience |volume=35 |issue=5 |pages=742–762 |doi=10.1111/j.1460-9568.2011.07987.x |pmid=22324876 |s2cid=4694570 |url=https://semanticscholar.org/paper/caa784fc3c22656413143559c402b54d0567f4d1 }}</ref><br /> * Performing a [[Fourier transform]] to investigate the series in the [[frequency domain]]<br /> * Use of a [[digital filter|filter]] to remove unwanted [[noise (physics)|noise]]<br /> * [[Principal component analysis]] (or [[empirical orthogonal function]] analysis)<br /> * [[Singular spectrum analysis]]<br /> * "Structural" models:<br /> ** General [[State Space Model]]s<br /> ** Unobserved Components Models<br /> * [[Machine Learning]]<br /> ** [[Artificial neural network]]s<br /> ** [[Support vector machine]]<br /> ** [[Fuzzy logic]]<br /> ** [[Gaussian process]]<br /> ** [[Genetic Programming]]<br /> ** [[Gene expression programming]]<br /> ** [[Hidden Markov model]]<br /> ** [[Multi expression programming]]<br /> * [[Queueing theory]] analysis<br /> * [[Control chart]]<br /> ** [[Shewhart individuals control chart]]<br /> ** [[CUSUM]] chart<br /> ** [[EWMA chart]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Nonlinear mixed-effects model|Nonlinear mixed-effects modeling]]<br /> * [[Dynamic time warping]]<ref name="Sakoe 1978">{{cite book |last1=Sakoe |first1=Hiroaki |last2=Chiba |first2=Seibi |year=1978 |chapter=Dynamic programming algorithm optimization for spoken word recognition |volume=26 |pages=43–49 |doi=10.1109/TASSP.1978.1163055 |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |s2cid=17900407 |chapter-url=https://semanticscholar.org/paper/18f355d7ef4aa9f82bf5c00f84e46714efa5fd77 }}</ref><br /> * [[Cross-correlation]]<ref>{{cite book |last1=Goutte |first1=Cyril |last2=Toft |first2=Peter |last3=Rostrup |first3=Egill |last4=Nielsen |first4=Finn Å. |last5=Hansen |first5=Lars Kai |year=1999 |chapter=On Clustering fMRI Time Series |volume=9 |issue=3 |pages=298–310 |doi=10.1006/nimg.1998.0391 |pmid=10075900 |journal=NeuroImage |s2cid=14147564 |chapter-url=https://semanticscholar.org/paper/2d5c663fb53d8348bdf3c4df0f881b5db2dcf5e3 }}</ref><br /> * [[Dynamic Bayesian network]]<br /> * [[Time-frequency representation|Time-frequency analysis techniques:]]<br /> ** [[Fast Fourier transform]]<br /> ** [[Continuous wavelet transform]]<br /> ** [[Short-time Fourier transform]]<br /> ** [[Chirplet transform]]<br /> ** [[Fractional Fourier transform]]<br /> * [[Chaos theory|Chaotic analysis]]<br /> ** [[Correlation dimension]]<br /> ** [[Recurrence plot]]s<br /> ** [[Recurrence quantification analysis]]<br /> ** [[Lyapunov exponent]]s<br /> ** [[Entropy encoding]]<br /> <br /> * Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions)<br /> * Scaled cross- and auto-correlation functions to remove contributions of slow components<br /> * Performing a Fourier transform to investigate the series in the frequency domain<br /> * Use of a filter to remove unwanted noise<br /> * Principal component analysis (or empirical orthogonal function analysis)<br /> * Singular spectrum analysis<br /> * "Structural" models:<br /> ** General State Space Models<br /> ** Unobserved Components Models<br /> * Machine Learning<br /> ** Artificial neural networks<br /> ** Support vector machine<br /> ** Fuzzy logic<br /> ** Gaussian process<br /> ** Genetic Programming<br /> ** Gene expression programming<br /> ** Hidden Markov model<br /> ** Multi expression programming<br /> * Queueing theory analysis<br /> * Control chart<br /> ** Shewhart individuals control chart<br /> ** CUSUM chart<br /> ** EWMA chart<br /> * Detrended fluctuation analysis<br /> * Nonlinear mixed-effects modeling<br /> * Dynamic time warping<br /> * Cross-correlation<br /> * Dynamic Bayesian network<br /> * Time-frequency analysis techniques:<br /> ** Fast Fourier transform<br /> ** Continuous wavelet transform<br /> ** Short-time Fourier transform<br /> ** Chirplet transform<br /> ** Fractional Fourier transform<br /> * Chaotic analysis<br /> ** Correlation dimension<br /> ** Recurrence plots<br /> ** Recurrence quantification analysis<br /> ** Lyapunov exponents<br /> ** Entropy encoding<br /> <br /> <br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数) <br /> * 调整互相关函数和自相关函数以去除慢分量的贡献 <br /> * 在频域中执行一个傅里叶变换来调查这个序列 <br /> * 使用<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图 <br /> * <br /> * EWMA 图 <br /> * 非趋势波动分析 <br /> * 非线性混合效应建模 <br /> * <br /> * 动态时间规整互相关 <br /> * <br /> * 动态贝氏网路 <br /> * 时频分析技术: <br /> * <br /> * 快速傅里叶变换连续小波转换 <br /> * <br /> * 短时距傅里叶变换 <br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析 <br /> * <br /> * <br /> * 复发图 <br /> * <br /> * 递归量化分析 <br /> * <br /> * Lyapunov 指数 <br /> * <br /> * <br /> * <br /> * <br /> <br /> ===Measures===<br /> Time series metrics or [[Features (pattern recognition)|features]] that can be used for time series [[Classification (machine learning)|classification]] or [[regression analysis]]:<ref>{{cite journal |last1=Mormann |first1=Florian |last2=Andrzejak |first2=Ralph G. |last3=Elger |first3=Christian E. |last4=Lehnertz |first4=Klaus |title=Seizure prediction: the long and winding road |journal=[[Brain (journal)|Brain]] |year=2007 |volume=130 |issue=2 |pages=314–333 |doi=10.1093/brain/awl241 |pmid=17008335|doi-access=free }}</ref><br /> <br /> Time series metrics or features that can be used for time series classification or regression analysis:<br /> <br /> = = = = 可用于时间序列分类或回归分析的时间序列度量或特征:<br /> <br /> * '''Univariate linear measures'''<br /> ** [[Moment (mathematics)]]<br /> ** [[Spectral band power]]<br /> ** [[Spectral edge frequency]]<br /> ** Accumulated [[Energy (signal processing)]]<br /> ** Characteristics of the [[autocorrelation]] function<br /> ** [[Hjorth parameters]]<br /> ** [[Fast Fourier transform|FFT]] parameters<br /> ** [[Autoregressive model]] parameters<br /> ** [[Mann–Kendall test]]<br /> * '''Univariate non-linear measures'''<br /> ** Measures based on the [[correlation]] sum<br /> ** [[Correlation dimension]]<br /> ** [[Correlation integral]]<br /> ** [[Correlation density]]<br /> ** [[Correlation entropy]]<br /> ** [[Approximate entropy]]<ref>{{cite web |last1=Land |first1=Bruce |last2=Elias |first2=Damian |title=Measuring the 'Complexity' of a time series |url=http://www.nbb.cornell.edu/neurobio/land/PROJECTS/Complexity/ }}</ref><br /> ** [[Sample entropy]]<br /> ** {{iw2|Fourier entropy||uk|Ентропія Фур'є}}<br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** [[Rényi entropy]]<br /> ** Higher-order methods<br /> ** [[Marginal predictability]]<br /> ** [[Dynamical similarity]] index<br /> ** [[State space]] dissimilarity measures<br /> ** [[Lyapunov exponent]]<br /> ** Permutation methods<br /> ** [[Local flow]]<br /> * '''Other univariate measures'''<br /> ** [[Algorithmic information theory|Algorithmic complexity]]<br /> ** [[Kolmogorov complexity]] estimates<br /> ** [[Hidden Markov Model]] states<br /> ** [[Rough path#Signature|Rough path signature]]<ref>[1] Chevyrev, I., Kormilitzin, A. (2016) "[https://arxiv.org/abs/1603.03788 A Primer on the Signature Method in Machine Learning], arXiv:1603.03788v1"</ref><br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * '''Bivariate linear measures'''<br /> ** Maximum linear [[cross-correlation]]<br /> ** Linear [[Coherence (signal processing)]]<br /> * '''Bivariate non-linear measures'''<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for [[Phase synchronization]]<br /> ** Measures for [[Phase locking]]<br /> * '''Similarity measures''':<ref>{{cite journal |last1=Ropella |first1=G. E. P. |last2=Nag |first2=D. A. |last3=Hunt |first3=C. A. |title=Similarity measures for automated comparison of in silico and in vitro experimental results |journal=Engineering in Medicine and Biology Society |year=2003 |volume=3 |pages=2933–2936 |doi=10.1109/IEMBS.2003.1280532 |isbn=978-0-7803-7789-9 |s2cid=17798157 }}</ref><br /> ** [[Cross-correlation]]<br /> ** [[Dynamic Time Warping]]<ref name="Sakoe 1978"/><br /> ** [[Hidden Markov Models]]<br /> ** [[Edit distance]]<br /> ** [[Total correlation]]<br /> ** [[Newey–West estimator]]<br /> ** [[Prais–Winsten estimation|Prais–Winsten transformation]]<br /> ** Data as Vectors in a Metrizable Space<br /> *** [[Minkowski distance]]<br /> *** [[Mahalanobis distance]]<br /> ** Data as time series with envelopes<br /> *** Global [[standard deviation]]<br /> *** Local [[standard deviation]]<br /> *** Windowed [[standard deviation]]<br /> ** Data interpreted as stochastic series<br /> *** [[Pearson product-moment correlation coefficient]]<br /> *** [[Spearman's rank correlation coefficient]]<br /> ** Data interpreted as a [[probability distribution]] function<br /> *** [[Kolmogorov–Smirnov test]]<br /> *** [[Cramér–von Mises criterion]]<br /> <br /> * Univariate linear measures<br /> ** Moment (mathematics)<br /> ** Spectral band power<br /> ** Spectral edge frequency<br /> ** Accumulated Energy (signal processing)<br /> ** Characteristics of the autocorrelation function<br /> ** Hjorth parameters<br /> ** FFT parameters<br /> ** Autoregressive model parameters<br /> ** Mann–Kendall test<br /> * Univariate non-linear measures<br /> ** Measures based on the correlation sum<br /> ** Correlation dimension<br /> ** Correlation integral<br /> ** Correlation density<br /> ** Correlation entropy<br /> ** Approximate entropy<br /> ** Sample entropy<br /> ** <br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** Rényi entropy<br /> ** Higher-order methods<br /> ** Marginal predictability<br /> ** Dynamical similarity index<br /> ** State space dissimilarity measures<br /> ** Lyapunov exponent<br /> ** Permutation methods<br /> ** Local flow<br /> * Other univariate measures<br /> ** Algorithmic complexity<br /> ** Kolmogorov complexity estimates<br /> ** Hidden Markov Model states<br /> ** Rough path signature[1] Chevyrev, I., Kormilitzin, A. (2016) "A Primer on the Signature Method in Machine Learning, arXiv:1603.03788v1"<br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * Bivariate linear measures<br /> ** Maximum linear cross-correlation<br /> ** Linear Coherence (signal processing)<br /> * Bivariate non-linear measures<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for Phase synchronization<br /> ** Measures for Phase locking<br /> * Similarity measures:<br /> ** Cross-correlation<br /> ** Dynamic Time Warping<br /> ** Hidden Markov Models<br /> ** Edit distance<br /> ** Total correlation<br /> ** Newey–West estimator<br /> ** Prais–Winsten transformation<br /> ** Data as Vectors in a Metrizable Space<br /> *** Minkowski distance<br /> *** Mahalanobis distance<br /> ** Data as time series with envelopes<br /> *** Global standard deviation<br /> *** Local standard deviation<br /> *** Windowed standard deviation<br /> ** Data interpreted as stochastic series<br /> *** Pearson product-moment correlation coefficient<br /> *** Spearman's rank correlation coefficient<br /> ** Data interpreted as a probability distribution function<br /> *** Kolmogorov–Smirnov test<br /> *** Cramér–von Mises criterion<br /> <br /> <br /> * 单变量线性测量 <br /> * <br /> * 矩(数学) <br /> * <br /> * 谱带功率 <br /> * <br /> * 谱边缘频率 <br /> * <br /> * 累积能量(信号处理) <br /> * <br /> * 自相关函数特性 <br /> * <br /> * Hjorth 参数 <br /> * <br /> * FFT 参数 <br /> * <br /> * 自回归模型参数 <br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流 <br /> * 其他单变量度量 <br /> * <br /> * 算法复杂度 <br /> * <br /> * 柯氏复杂性估计 <br /> * <br /> * 隐马尔可夫模型状态 <br /> * <br /> * 粗糙路径签名[1] Chevyrev，i. ，Kormilitzin，a。(2016)“ a Primer on the Signature Method in Machine Learning，arXiv: 1603.03788 v1”<br /> * <br /> * 替代时间序列和替代校正 <br /> * <br /> * 递归损失(非平稳度) <br /> * 双变量线性度量 <br /> * <br /> * 最大线性互相关 <br /> * <br /> * 线性相干性(信号处理) <br /> * 双变量非线性度量 <br /> * <br /> * 非线性相互依赖 <br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学) <br /> * <br /> * 相位同步的度量 <br /> * <br /> * 相位锁定的度量 <br /> * <br /> * 相似度量: <br /> * <br /> * 互相关 <br /> * <br /> * <br /> * 动态时间规整 <br /> * <br /> * <br /> * 隐马尔可夫模型 <br /> * <br /> * <br /> * 编辑距离 <br /> * <br /> * 总相关性 <br /> * <br /> * Newey-West 估计 <br /> * <br /> * Prais-Winsten 变换 <br /> * <br /> * 数据作为向量在乌雷松度量化定理 <br /> * <br /> * <br /> * 明氏距离 <br /> * <br /> * 马氏距离 <br /> * <br /> * 数据作为时间序列与信封 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差标准差 <br /> * <br /> * <br /> * 窗口标准差 <br /> * <br /> * 数据解释为随机序列 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数 <br /> * <br /> * 数据解释为概率分布函数 <br /> * <br /> * Kolmogorov-Smirnov 检验 <br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ==Visualization==<br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<ref>{{cite web|last1=Tominski|first1=Christian|last2= Aigner|first2=Wolfgang|title=The TimeViz Browser:A Visual Survey of Visualization Techniques for Time-Oriented Data|url=http://survey.timeviz.net/|access-date=1 June 2014}}</ref><br /> <br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<br /> <br /> = = 可视化 = = 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> ===Overlapping charts===<br /> * [[Braided graphs]]<br /> * Line charts<br /> * Slope graphs<br /> * {{iw2|GapChart||fr}}<br /> <br /> * Braided graphs<br /> * Line charts<br /> * Slope graphs<br /> * <br /> <br /> = = = = 重叠图 = = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> ===Separated charts===<br /> * [[Horizon graphs]]<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> * Horizon graphs<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> = = = = = 分离图表 = = = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ==See also==<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ==References==<br /> {{Reflist|2}}<br /> <br /> ==Further reading==<br /> * {{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> * [[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> * {{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> * {{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> * [[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]]. {{ISBN|978-0-12-564901-8}}<br /> * {{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer, {{ISBN|978-3-319-52451-1}}<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> * [[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> * {{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> = = 进一步阅读 = = <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社。<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社。<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去。北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社。<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社。<br /> *<br /> <br /> ==External links==<br /> {{Commons category}}<br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> <br /> *Introduction to Time series Analysis (Engineering Statistics Handbook) — A practical guide to Time series analysis.<br /> <br /> = = 外部链接 = = <br /> * 时间序列分析导论(工程统计手册)ー时间序列分析实用指南。<br /> <br /> {{Statistics}}<br /> {{Portal bar|Mathematics}}<br /> {{Authority control}}<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> <br /> <br /> <br /> Category:Statistical data types<br /> Category:Mathematical and quantitative methods (economics)<br /> Category:Machine learning<br /> <br /> 类别: 统计数据类型类别: 数学和定量方法(经济学)类别: 机器学习<br /> <br /> <noinclude><br /> <br /> <small>This page was moved from [[wikipedia:en:Time series]]. Its edit history can be viewed at [[时间序列分析/edithistory]]</small></noinclude><br /> <br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33958 时间序列分析 2023-02-11T13:25:24Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数值Numeric数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ===分析方法===<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些模型中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ===面板数据===<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==='''分析'''===<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===时间序列分析在信号处理上的应用===<br /> {{see also|Signal processing|Estimation theory}}<br /> 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，该方法在二战期间迅速得以推广。数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯和其他学者完成了信号的滤波处理，且预测了在特定时间段中的信号值。相关知识参见卡尔曼滤波器，参数估测和数字信号处理的介绍。<br /> ===时间序列的分割处理===<br /> {{main|Time-series segmentation}}<br /> <br /> <br /> 时间序列的分割处理是将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。时间序列分割的目标是识别时间序列中的分段临界点，并分析每个分段的动态特性。此外，时间序列可以建模成一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ===模型 ===<br /> <br /> <br /> 时间序列数据的模型可以用多种形式来表示不同的随机过程。在对过程层次的变化进行建模时，三大重要模型是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个模型线性地依赖于以前的数据点。这些模型的结合产生了自回归移动平均(ARMA)和模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对三大重要模型进行了推广。处理矢量值数据的模型的扩展可以在多元时间序列模型下继续完成，有一些是前面的首字母缩略词被扩展，例如一个初始的“ v”代表“矢量”； VAR 代表向量自回归模型。从这些模型的另外一组扩展可以发现观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应)；与多变量情况的区别在于这种强迫序列可能是在实验者的控制之下所得到的。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> <br /> 研究数据对过往的数据点的非线性依赖关系是有趣的，主要是它有产生混沌时间序列的可能性。然而，更重要的是，使用来自非线性模型的预测优于来自线性模型的预测。例如非线性自回归外生模型的预测准确度优于线性的回顾模型。 <br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time (heteroskedasticity). These models represent autoregressive conditional heteroskedasticity (ARCH) and the collection comprises a wide variety of representation (GARCH, TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a doubly stochastic model.<br /> <br /> 在其他的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型有ARCH模型，其中包括GARCH，TARCH，EGARCH，FIGARCH，CGARCH 等等。在这里，变异性的变化与观测系列的最近过去的值有关，或者是预测的。这与局部变化的其他可能表现形式形成对比，在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also [[Markov switching multifractal]] (MSMF) techniques for modeling volatility evolution.<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution.<br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列，试图说明在多个尺度上的时间依赖。参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> A [[Hidden Markov model]] (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest [[dynamic Bayesian network]]. HMM models are widely used in [[speech recognition]], for translating a time series of spoken words into text.<br /> <br /> A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.<br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔科姆可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，用于将语音序列转换成文本。<br /> <br /> ===Notation===<br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series ''X'' that is indexed by the [[natural number]]s is written<br /> :''X'' = (''X''<sub>1</sub>, ''X''<sub>2</sub>, ...).<br /> <br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written<br /> :X = (X1, X2, ...).<br /> <br /> = = = 表示法 = = 用于时间序列分析的许多不同的表示法。一个用于指定时间序列 x 的通用符号是: x = (X1，X2，...)。<br /> <br /> Another common notation is<br /> :''Y'' = (''Y<sub>t</sub>'': ''t'' ∈ ''T''),<br /> where ''T'' is the [[index set]].<br /> <br /> Another common notation is<br /> :Y = (Yt: t ∈ T),<br /> where T is the index set.<br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===Conditions===<br /> There are two sets of conditions under which much of the theory is built:<br /> * [[Stationary process]]<br /> * [[Ergodic process]]<br /> <br /> There are two sets of conditions under which much of the theory is built:<br /> * Stationary process<br /> * Ergodic process<br /> <br /> 这个理论的大部分建立在两个条件之下: <br /> * 平稳过程遍历过程<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: [[strict stationarity]] and [[Stationary process#Weaker forms of stationarity|second-order stationarity]]. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: strict stationarity and second-order stationarity. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> 然而，平稳性的概念必须扩展到考虑两个重要的概念: 严格平稳性和二阶平稳性。模型和应用程序都可以在这些条件中的每一种情况下开发，尽管后一种情况下的模型可能被认为只是部分具体说明。<br /> <br /> In addition, time-series analysis can be applied where the series are [[Cyclostationary process|seasonally stationary]] or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in [[time-frequency analysis]] which makes use of a [[time–frequency representation]] of a time-series or signal.<ref>Boashash, B. (ed.), (2003) ''Time-Frequency Signal Analysis and Processing: A Comprehensive Reference'', Elsevier Science, Oxford, 2003 {{isbn|0-08-044335-4}}</ref><br /> <br /> In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.Boashash, B. (ed.), (2003) Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003 <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或非平稳的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。波阿什，b。我不知道你在说什么。) ，(2003)《时频信号分析与处理: 综合参考》，爱思唯尔科学出版社，牛津，2003<br /> <br /> ===Tools===<br /> Tools for investigating time-series data include:<br /> <br /> Tools for investigating time-series data include:<br /> <br /> = = = 调查时间序列数据的工具包括:<br /> <br /> * Consideration of the [[autocorrelation|autocorrelation function]] and the [[Spectral density|spectral density function]] (also [[cross-correlation function]]s and cross-spectral density functions)<br /> * [[Scaled correlation|Scaled]] cross- and auto-correlation functions to remove contributions of slow components<ref name="Nikolicetal">{{cite journal |last1=Nikolić |first1=D. |last2=Muresan |first2=R. C. |last3=Feng |first3=W. |last4=Singer |first4=W. |year=2012 |title=Scaled correlation analysis: a better way to compute a cross-correlogram |journal=European Journal of Neuroscience |volume=35 |issue=5 |pages=742–762 |doi=10.1111/j.1460-9568.2011.07987.x |pmid=22324876 |s2cid=4694570 |url=https://semanticscholar.org/paper/caa784fc3c22656413143559c402b54d0567f4d1 }}</ref><br /> * Performing a [[Fourier transform]] to investigate the series in the [[frequency domain]]<br /> * Use of a [[digital filter|filter]] to remove unwanted [[noise (physics)|noise]]<br /> * [[Principal component analysis]] (or [[empirical orthogonal function]] analysis)<br /> * [[Singular spectrum analysis]]<br /> * "Structural" models:<br /> ** General [[State Space Model]]s<br /> ** Unobserved Components Models<br /> * [[Machine Learning]]<br /> ** [[Artificial neural network]]s<br /> ** [[Support vector machine]]<br /> ** [[Fuzzy logic]]<br /> ** [[Gaussian process]]<br /> ** [[Genetic Programming]]<br /> ** [[Gene expression programming]]<br /> ** [[Hidden Markov model]]<br /> ** [[Multi expression programming]]<br /> * [[Queueing theory]] analysis<br /> * [[Control chart]]<br /> ** [[Shewhart individuals control chart]]<br /> ** [[CUSUM]] chart<br /> ** [[EWMA chart]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Nonlinear mixed-effects model|Nonlinear mixed-effects modeling]]<br /> * [[Dynamic time warping]]<ref name="Sakoe 1978">{{cite book |last1=Sakoe |first1=Hiroaki |last2=Chiba |first2=Seibi |year=1978 |chapter=Dynamic programming algorithm optimization for spoken word recognition |volume=26 |pages=43–49 |doi=10.1109/TASSP.1978.1163055 |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |s2cid=17900407 |chapter-url=https://semanticscholar.org/paper/18f355d7ef4aa9f82bf5c00f84e46714efa5fd77 }}</ref><br /> * [[Cross-correlation]]<ref>{{cite book |last1=Goutte |first1=Cyril |last2=Toft |first2=Peter |last3=Rostrup |first3=Egill |last4=Nielsen |first4=Finn Å. |last5=Hansen |first5=Lars Kai |year=1999 |chapter=On Clustering fMRI Time Series |volume=9 |issue=3 |pages=298–310 |doi=10.1006/nimg.1998.0391 |pmid=10075900 |journal=NeuroImage |s2cid=14147564 |chapter-url=https://semanticscholar.org/paper/2d5c663fb53d8348bdf3c4df0f881b5db2dcf5e3 }}</ref><br /> * [[Dynamic Bayesian network]]<br /> * [[Time-frequency representation|Time-frequency analysis techniques:]]<br /> ** [[Fast Fourier transform]]<br /> ** [[Continuous wavelet transform]]<br /> ** [[Short-time Fourier transform]]<br /> ** [[Chirplet transform]]<br /> ** [[Fractional Fourier transform]]<br /> * [[Chaos theory|Chaotic analysis]]<br /> ** [[Correlation dimension]]<br /> ** [[Recurrence plot]]s<br /> ** [[Recurrence quantification analysis]]<br /> ** [[Lyapunov exponent]]s<br /> ** [[Entropy encoding]]<br /> <br /> * Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions)<br /> * Scaled cross- and auto-correlation functions to remove contributions of slow components<br /> * Performing a Fourier transform to investigate the series in the frequency domain<br /> * Use of a filter to remove unwanted noise<br /> * Principal component analysis (or empirical orthogonal function analysis)<br /> * Singular spectrum analysis<br /> * "Structural" models:<br /> ** General State Space Models<br /> ** Unobserved Components Models<br /> * Machine Learning<br /> ** Artificial neural networks<br /> ** Support vector machine<br /> ** Fuzzy logic<br /> ** Gaussian process<br /> ** Genetic Programming<br /> ** Gene expression programming<br /> ** Hidden Markov model<br /> ** Multi expression programming<br /> * Queueing theory analysis<br /> * Control chart<br /> ** Shewhart individuals control chart<br /> ** CUSUM chart<br /> ** EWMA chart<br /> * Detrended fluctuation analysis<br /> * Nonlinear mixed-effects modeling<br /> * Dynamic time warping<br /> * Cross-correlation<br /> * Dynamic Bayesian network<br /> * Time-frequency analysis techniques:<br /> ** Fast Fourier transform<br /> ** Continuous wavelet transform<br /> ** Short-time Fourier transform<br /> ** Chirplet transform<br /> ** Fractional Fourier transform<br /> * Chaotic analysis<br /> ** Correlation dimension<br /> ** Recurrence plots<br /> ** Recurrence quantification analysis<br /> ** Lyapunov exponents<br /> ** Entropy encoding<br /> <br /> <br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数) <br /> * 调整互相关函数和自相关函数以去除慢分量的贡献 <br /> * 在频域中执行一个傅里叶变换来调查这个序列 <br /> * 使用<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图 <br /> * <br /> * EWMA 图 <br /> * 非趋势波动分析 <br /> * 非线性混合效应建模 <br /> * <br /> * 动态时间规整互相关 <br /> * <br /> * 动态贝氏网路 <br /> * 时频分析技术: <br /> * <br /> * 快速傅里叶变换连续小波转换 <br /> * <br /> * 短时距傅里叶变换 <br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析 <br /> * <br /> * <br /> * 复发图 <br /> * <br /> * 递归量化分析 <br /> * <br /> * Lyapunov 指数 <br /> * <br /> * <br /> * <br /> * <br /> <br /> ===Measures===<br /> Time series metrics or [[Features (pattern recognition)|features]] that can be used for time series [[Classification (machine learning)|classification]] or [[regression analysis]]:<ref>{{cite journal |last1=Mormann |first1=Florian |last2=Andrzejak |first2=Ralph G. |last3=Elger |first3=Christian E. |last4=Lehnertz |first4=Klaus |title=Seizure prediction: the long and winding road |journal=[[Brain (journal)|Brain]] |year=2007 |volume=130 |issue=2 |pages=314–333 |doi=10.1093/brain/awl241 |pmid=17008335|doi-access=free }}</ref><br /> <br /> Time series metrics or features that can be used for time series classification or regression analysis:<br /> <br /> = = = = 可用于时间序列分类或回归分析的时间序列度量或特征:<br /> <br /> * '''Univariate linear measures'''<br /> ** [[Moment (mathematics)]]<br /> ** [[Spectral band power]]<br /> ** [[Spectral edge frequency]]<br /> ** Accumulated [[Energy (signal processing)]]<br /> ** Characteristics of the [[autocorrelation]] function<br /> ** [[Hjorth parameters]]<br /> ** [[Fast Fourier transform|FFT]] parameters<br /> ** [[Autoregressive model]] parameters<br /> ** [[Mann–Kendall test]]<br /> * '''Univariate non-linear measures'''<br /> ** Measures based on the [[correlation]] sum<br /> ** [[Correlation dimension]]<br /> ** [[Correlation integral]]<br /> ** [[Correlation density]]<br /> ** [[Correlation entropy]]<br /> ** [[Approximate entropy]]<ref>{{cite web |last1=Land |first1=Bruce |last2=Elias |first2=Damian |title=Measuring the 'Complexity' of a time series |url=http://www.nbb.cornell.edu/neurobio/land/PROJECTS/Complexity/ }}</ref><br /> ** [[Sample entropy]]<br /> ** {{iw2|Fourier entropy||uk|Ентропія Фур'є}}<br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** [[Rényi entropy]]<br /> ** Higher-order methods<br /> ** [[Marginal predictability]]<br /> ** [[Dynamical similarity]] index<br /> ** [[State space]] dissimilarity measures<br /> ** [[Lyapunov exponent]]<br /> ** Permutation methods<br /> ** [[Local flow]]<br /> * '''Other univariate measures'''<br /> ** [[Algorithmic information theory|Algorithmic complexity]]<br /> ** [[Kolmogorov complexity]] estimates<br /> ** [[Hidden Markov Model]] states<br /> ** [[Rough path#Signature|Rough path signature]]<ref>[1] Chevyrev, I., Kormilitzin, A. (2016) "[https://arxiv.org/abs/1603.03788 A Primer on the Signature Method in Machine Learning], arXiv:1603.03788v1"</ref><br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * '''Bivariate linear measures'''<br /> ** Maximum linear [[cross-correlation]]<br /> ** Linear [[Coherence (signal processing)]]<br /> * '''Bivariate non-linear measures'''<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for [[Phase synchronization]]<br /> ** Measures for [[Phase locking]]<br /> * '''Similarity measures''':<ref>{{cite journal |last1=Ropella |first1=G. E. P. |last2=Nag |first2=D. A. |last3=Hunt |first3=C. A. |title=Similarity measures for automated comparison of in silico and in vitro experimental results |journal=Engineering in Medicine and Biology Society |year=2003 |volume=3 |pages=2933–2936 |doi=10.1109/IEMBS.2003.1280532 |isbn=978-0-7803-7789-9 |s2cid=17798157 }}</ref><br /> ** [[Cross-correlation]]<br /> ** [[Dynamic Time Warping]]<ref name="Sakoe 1978"/><br /> ** [[Hidden Markov Models]]<br /> ** [[Edit distance]]<br /> ** [[Total correlation]]<br /> ** [[Newey–West estimator]]<br /> ** [[Prais–Winsten estimation|Prais–Winsten transformation]]<br /> ** Data as Vectors in a Metrizable Space<br /> *** [[Minkowski distance]]<br /> *** [[Mahalanobis distance]]<br /> ** Data as time series with envelopes<br /> *** Global [[standard deviation]]<br /> *** Local [[standard deviation]]<br /> *** Windowed [[standard deviation]]<br /> ** Data interpreted as stochastic series<br /> *** [[Pearson product-moment correlation coefficient]]<br /> *** [[Spearman's rank correlation coefficient]]<br /> ** Data interpreted as a [[probability distribution]] function<br /> *** [[Kolmogorov–Smirnov test]]<br /> *** [[Cramér–von Mises criterion]]<br /> <br /> * Univariate linear measures<br /> ** Moment (mathematics)<br /> ** Spectral band power<br /> ** Spectral edge frequency<br /> ** Accumulated Energy (signal processing)<br /> ** Characteristics of the autocorrelation function<br /> ** Hjorth parameters<br /> ** FFT parameters<br /> ** Autoregressive model parameters<br /> ** Mann–Kendall test<br /> * Univariate non-linear measures<br /> ** Measures based on the correlation sum<br /> ** Correlation dimension<br /> ** Correlation integral<br /> ** Correlation density<br /> ** Correlation entropy<br /> ** Approximate entropy<br /> ** Sample entropy<br /> ** <br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** Rényi entropy<br /> ** Higher-order methods<br /> ** Marginal predictability<br /> ** Dynamical similarity index<br /> ** State space dissimilarity measures<br /> ** Lyapunov exponent<br /> ** Permutation methods<br /> ** Local flow<br /> * Other univariate measures<br /> ** Algorithmic complexity<br /> ** Kolmogorov complexity estimates<br /> ** Hidden Markov Model states<br /> ** Rough path signature[1] Chevyrev, I., Kormilitzin, A. (2016) "A Primer on the Signature Method in Machine Learning, arXiv:1603.03788v1"<br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * Bivariate linear measures<br /> ** Maximum linear cross-correlation<br /> ** Linear Coherence (signal processing)<br /> * Bivariate non-linear measures<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for Phase synchronization<br /> ** Measures for Phase locking<br /> * Similarity measures:<br /> ** Cross-correlation<br /> ** Dynamic Time Warping<br /> ** Hidden Markov Models<br /> ** Edit distance<br /> ** Total correlation<br /> ** Newey–West estimator<br /> ** Prais–Winsten transformation<br /> ** Data as Vectors in a Metrizable Space<br /> *** Minkowski distance<br /> *** Mahalanobis distance<br /> ** Data as time series with envelopes<br /> *** Global standard deviation<br /> *** Local standard deviation<br /> *** Windowed standard deviation<br /> ** Data interpreted as stochastic series<br /> *** Pearson product-moment correlation coefficient<br /> *** Spearman's rank correlation coefficient<br /> ** Data interpreted as a probability distribution function<br /> *** Kolmogorov–Smirnov test<br /> *** Cramér–von Mises criterion<br /> <br /> <br /> * 单变量线性测量 <br /> * <br /> * 矩(数学) <br /> * <br /> * 谱带功率 <br /> * <br /> * 谱边缘频率 <br /> * <br /> * 累积能量(信号处理) <br /> * <br /> * 自相关函数特性 <br /> * <br /> * Hjorth 参数 <br /> * <br /> * FFT 参数 <br /> * <br /> * 自回归模型参数 <br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流 <br /> * 其他单变量度量 <br /> * <br /> * 算法复杂度 <br /> * <br /> * 柯氏复杂性估计 <br /> * <br /> * 隐马尔可夫模型状态 <br /> * <br /> * 粗糙路径签名[1] Chevyrev，i. ，Kormilitzin，a。(2016)“ a Primer on the Signature Method in Machine Learning，arXiv: 1603.03788 v1”<br /> * <br /> * 替代时间序列和替代校正 <br /> * <br /> * 递归损失(非平稳度) <br /> * 双变量线性度量 <br /> * <br /> * 最大线性互相关 <br /> * <br /> * 线性相干性(信号处理) <br /> * 双变量非线性度量 <br /> * <br /> * 非线性相互依赖 <br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学) <br /> * <br /> * 相位同步的度量 <br /> * <br /> * 相位锁定的度量 <br /> * <br /> * 相似度量: <br /> * <br /> * 互相关 <br /> * <br /> * <br /> * 动态时间规整 <br /> * <br /> * <br /> * 隐马尔可夫模型 <br /> * <br /> * <br /> * 编辑距离 <br /> * <br /> * 总相关性 <br /> * <br /> * Newey-West 估计 <br /> * <br /> * Prais-Winsten 变换 <br /> * <br /> * 数据作为向量在乌雷松度量化定理 <br /> * <br /> * <br /> * 明氏距离 <br /> * <br /> * 马氏距离 <br /> * <br /> * 数据作为时间序列与信封 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差标准差 <br /> * <br /> * <br /> * 窗口标准差 <br /> * <br /> * 数据解释为随机序列 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数 <br /> * <br /> * 数据解释为概率分布函数 <br /> * <br /> * Kolmogorov-Smirnov 检验 <br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ==Visualization==<br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<ref>{{cite web|last1=Tominski|first1=Christian|last2= Aigner|first2=Wolfgang|title=The TimeViz Browser:A Visual Survey of Visualization Techniques for Time-Oriented Data|url=http://survey.timeviz.net/|access-date=1 June 2014}}</ref><br /> <br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<br /> <br /> = = 可视化 = = 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> ===Overlapping charts===<br /> * [[Braided graphs]]<br /> * Line charts<br /> * Slope graphs<br /> * {{iw2|GapChart||fr}}<br /> <br /> * Braided graphs<br /> * Line charts<br /> * Slope graphs<br /> * <br /> <br /> = = = = 重叠图 = = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> ===Separated charts===<br /> * [[Horizon graphs]]<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> * Horizon graphs<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> = = = = = 分离图表 = = = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ==See also==<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ==References==<br /> {{Reflist|2}}<br /> <br /> ==Further reading==<br /> * {{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> * [[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> * {{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> * {{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> * [[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]]. {{ISBN|978-0-12-564901-8}}<br /> * {{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer, {{ISBN|978-3-319-52451-1}}<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> * [[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> * {{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> = = 进一步阅读 = = <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社。<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社。<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去。北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社。<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社。<br /> *<br /> <br /> ==External links==<br /> {{Commons category}}<br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> <br /> *Introduction to Time series Analysis (Engineering Statistics Handbook) — A practical guide to Time series analysis.<br /> <br /> = = 外部链接 = = <br /> * 时间序列分析导论(工程统计手册)ー时间序列分析实用指南。<br /> <br /> {{Statistics}}<br /> {{Portal bar|Mathematics}}<br /> {{Authority control}}<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> <br /> <br /> <br /> Category:Statistical data types<br /> Category:Mathematical and quantitative methods (economics)<br /> Category:Machine learning<br /> <br /> 类别: 统计数据类型类别: 数学和定量方法(经济学)类别: 机器学习<br /> <br /> <noinclude><br /> <br /> <small>This page was moved from [[wikipedia:en:Time series]]. Its edit history can be viewed at [[时间序列分析/edithistory]]</small></noinclude><br /> <br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33957 时间序列分析 2023-02-08T13:13:11Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数值Numeric数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ==分析方法==<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些方法中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ==面板数据==<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==分析==<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> 在统计学中，预测是统计学的推理环节的一部分。有一种推理方法是预测推理，这种预测可以与几种统计学推理方法混合使用。统计学的预测方法之一是将部分样本数值扩大到整体去分析。这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，推测特定时间点信息的状态的个过程就被称为预测。<br /> * 为完成随机模拟而建立完整的统计模型能产生时间序列的替代版本，会反映未来在非特定时间段内可能发生的情况。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===Classification===<br /> {{main|Statistical classification}}<br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in [[sign language]].<br /> <br /> <br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in sign language.<br /> <br /> = = = 分类 = = 将时间序列模式分配到一个特定的类别，例如根据手语中的一系列动作识别一个单词。<br /> <br /> ===Signal estimation===<br /> {{see also|Signal processing|Estimation theory}}<br /> This approach is based on [[harmonic analysis]] and filtering of signals in the [[frequency domain]] using the [[Fourier transform]], and [[spectral density estimation]], the development of which was significantly accelerated during [[World War II]] by mathematician [[Norbert Wiener]], electrical engineers [[Rudolf E. Kálmán]], [[Dennis Gabor]] and others for filtering signals from noise and predicting signal values at a certain point in time. See [[Kalman filter]], [[Estimation theory]], and [[Digital signal processing]]<br /> <br /> <br /> This approach is based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation, the development of which was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. See Kalman filter, Estimation theory, and Digital signal processing<br /> <br /> = = = 信号估计 = = = 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，其发展是显着加速二战期间由数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯 Gabor 和其他人从噪音信号过滤和预测信号值在一定时间点。参见卡尔曼滤波器，参数估测和数字信号处理<br /> <br /> ===Segmentation===<br /> {{main|Time-series segmentation}}<br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using [[Change detection|change-point detection]], or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> <br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using change-point detection, or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> = = = 分割 = = 将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。在时间序列分割中，目标是识别时间序列中的分段边界点，并刻画每个分段的动态特性。人们可以通过变点检测来解决这个问题，或者将时间序列建模为一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ==Models==<br /> <br /> ==Models==<br /> <br /> = = 模型 = = <br /> <br /> Models for time series data can have many forms and represent different [[stochastic processes]]. When modeling variations in the level of a process, three broad classes of practical importance are the ''[[autoregressive]]'' (AR) models, the ''integrated'' (I) models, and the ''[[moving average model|moving average]]'' (MA) models. These three classes depend linearly on previous data points.<ref name="linear time series">{{cite book |author-link=Neil Gershenfeld |last=Gershenfeld |first=N. |year=1999 |title=The Nature of Mathematical Modeling |url=https://archive.org/details/naturemathematic00gers_334 |url-access=limited |location=New York |publisher=Cambridge University Press |pages=[https://archive.org/details/naturemathematic00gers_334/page/n206 205]–208 |isbn=978-0521570954 }}</ref> Combinations of these ideas produce [[autoregressive moving average]] (ARMA) and [[autoregressive integrated moving average]] (ARIMA) models. The [[autoregressive fractionally integrated moving average]] (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for [[vector autoregression]]. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> Models for time series data can have many forms and represent different stochastic processes. When modeling variations in the level of a process, three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. These three classes depend linearly on previous data points. Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models. The autoregressive fractionally integrated moving average (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector autoregression. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> 时间序列数据的模型可以有多种形式，表示不同的随机过程。在对过程层次的变化进行建模时，三大类实际的重要性是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个类线性地依赖于以前的数据点。这些想法的结合产生了自回归移动平均(ARMA)和 ARIMA模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对前三种模型进行了推广。处理矢量值数据的这些类的扩展可以在多元时间序列模型的标题下得到，有时前面的首字母缩略词被扩展，包括一个初始的“ v”代表“矢量”，如在 VAR 代表向量自回归模型。这些模型的另外一组扩展可用于观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应) : 与多变量情况的区别在于强迫序列可能是确定的或者在实验者的控制之下。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a [[chaos theory|chaotic]] time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in [[nonlinear autoregressive exogenous model]]s. Further references on nonlinear time series analysis: (Kantz and Schreiber),<ref>{{cite book|last1=Kantz|first1=Holger|last2=Thomas|first2=Schreiber|title=Nonlinear Time Series Analysis|date=2004|publisher=Cambridge University Press|location=London|isbn=978-0521529020}}</ref> and (Abarbanel)<ref>{{cite book|last1=Abarbanel|first1=Henry|title=Analysis of Observed Chaotic Data|date=Nov 25, 1997|publisher=Springer|location=New York|isbn=978-0387983721}}</ref><br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a chaotic time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in nonlinear autoregressive exogenous models. Further references on nonlinear time series analysis: (Kantz and Schreiber), and (Abarbanel)<br /> <br /> 一系列数据的水平对以前的数据点的非线性依赖是有趣的，部分是因为产生混沌时间序列的可能性。然而，更重要的是，经验调查可以表明使用来自非线性模型的预测优于来自线性模型的预测，例如在非线性自回归外生模型中。非线性时间序列分析的进一步参考文献: (Kantz 和 Schreiber)和(Abarbanel) <br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time ([[heteroskedasticity]]). These models represent [[autoregressive conditional heteroskedasticity]] (ARCH) and the collection comprises a wide variety of representation ([[GARCH]], TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a [[doubly stochastic model]].<br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time (heteroskedasticity). These models represent autoregressive conditional heteroskedasticity (ARCH) and the collection comprises a wide variety of representation (GARCH, TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a doubly stochastic model.<br /> <br /> 在其他类型的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型代表了 ARCH模型(ARCH) ，收藏包括各种各样的代表(GARCH，TARCH，EGARCH，FIGARCH，CGARCH 等等)。在这里，变异性的变化与观测系列的最近过去的值有关，或者是预测的。这与局部变化的其他可能表现形式形成对比，在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also [[Markov switching multifractal]] (MSMF) techniques for modeling volatility evolution.<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution.<br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列，试图说明在多个尺度上的时间依赖。参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> A [[Hidden Markov model]] (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest [[dynamic Bayesian network]]. HMM models are widely used in [[speech recognition]], for translating a time series of spoken words into text.<br /> <br /> A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.<br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔科姆可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，用于将语音序列转换成文本。<br /> <br /> ===Notation===<br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series ''X'' that is indexed by the [[natural number]]s is written<br /> :''X'' = (''X''<sub>1</sub>, ''X''<sub>2</sub>, ...).<br /> <br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written<br /> :X = (X1, X2, ...).<br /> <br /> = = = 表示法 = = 用于时间序列分析的许多不同的表示法。一个用于指定时间序列 x 的通用符号是: x = (X1，X2，...)。<br /> <br /> Another common notation is<br /> :''Y'' = (''Y<sub>t</sub>'': ''t'' ∈ ''T''),<br /> where ''T'' is the [[index set]].<br /> <br /> Another common notation is<br /> :Y = (Yt: t ∈ T),<br /> where T is the index set.<br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===Conditions===<br /> There are two sets of conditions under which much of the theory is built:<br /> * [[Stationary process]]<br /> * [[Ergodic process]]<br /> <br /> There are two sets of conditions under which much of the theory is built:<br /> * Stationary process<br /> * Ergodic process<br /> <br /> 这个理论的大部分建立在两个条件之下: <br /> * 平稳过程遍历过程<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: [[strict stationarity]] and [[Stationary process#Weaker forms of stationarity|second-order stationarity]]. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: strict stationarity and second-order stationarity. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> 然而，平稳性的概念必须扩展到考虑两个重要的概念: 严格平稳性和二阶平稳性。模型和应用程序都可以在这些条件中的每一种情况下开发，尽管后一种情况下的模型可能被认为只是部分具体说明。<br /> <br /> In addition, time-series analysis can be applied where the series are [[Cyclostationary process|seasonally stationary]] or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in [[time-frequency analysis]] which makes use of a [[time–frequency representation]] of a time-series or signal.<ref>Boashash, B. (ed.), (2003) ''Time-Frequency Signal Analysis and Processing: A Comprehensive Reference'', Elsevier Science, Oxford, 2003 {{isbn|0-08-044335-4}}</ref><br /> <br /> In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.Boashash, B. (ed.), (2003) Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003 <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或非平稳的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。波阿什，b。我不知道你在说什么。) ，(2003)《时频信号分析与处理: 综合参考》，爱思唯尔科学出版社，牛津，2003<br /> <br /> ===Tools===<br /> Tools for investigating time-series data include:<br /> <br /> Tools for investigating time-series data include:<br /> <br /> = = = 调查时间序列数据的工具包括:<br /> <br /> * Consideration of the [[autocorrelation|autocorrelation function]] and the [[Spectral density|spectral density function]] (also [[cross-correlation function]]s and cross-spectral density functions)<br /> * [[Scaled correlation|Scaled]] cross- and auto-correlation functions to remove contributions of slow components<ref name="Nikolicetal">{{cite journal |last1=Nikolić |first1=D. |last2=Muresan |first2=R. C. |last3=Feng |first3=W. |last4=Singer |first4=W. |year=2012 |title=Scaled correlation analysis: a better way to compute a cross-correlogram |journal=European Journal of Neuroscience |volume=35 |issue=5 |pages=742–762 |doi=10.1111/j.1460-9568.2011.07987.x |pmid=22324876 |s2cid=4694570 |url=https://semanticscholar.org/paper/caa784fc3c22656413143559c402b54d0567f4d1 }}</ref><br /> * Performing a [[Fourier transform]] to investigate the series in the [[frequency domain]]<br /> * Use of a [[digital filter|filter]] to remove unwanted [[noise (physics)|noise]]<br /> * [[Principal component analysis]] (or [[empirical orthogonal function]] analysis)<br /> * [[Singular spectrum analysis]]<br /> * "Structural" models:<br /> ** General [[State Space Model]]s<br /> ** Unobserved Components Models<br /> * [[Machine Learning]]<br /> ** [[Artificial neural network]]s<br /> ** [[Support vector machine]]<br /> ** [[Fuzzy logic]]<br /> ** [[Gaussian process]]<br /> ** [[Genetic Programming]]<br /> ** [[Gene expression programming]]<br /> ** [[Hidden Markov model]]<br /> ** [[Multi expression programming]]<br /> * [[Queueing theory]] analysis<br /> * [[Control chart]]<br /> ** [[Shewhart individuals control chart]]<br /> ** [[CUSUM]] chart<br /> ** [[EWMA chart]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Nonlinear mixed-effects model|Nonlinear mixed-effects modeling]]<br /> * [[Dynamic time warping]]<ref name="Sakoe 1978">{{cite book |last1=Sakoe |first1=Hiroaki |last2=Chiba |first2=Seibi |year=1978 |chapter=Dynamic programming algorithm optimization for spoken word recognition |volume=26 |pages=43–49 |doi=10.1109/TASSP.1978.1163055 |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |s2cid=17900407 |chapter-url=https://semanticscholar.org/paper/18f355d7ef4aa9f82bf5c00f84e46714efa5fd77 }}</ref><br /> * [[Cross-correlation]]<ref>{{cite book |last1=Goutte |first1=Cyril |last2=Toft |first2=Peter |last3=Rostrup |first3=Egill |last4=Nielsen |first4=Finn Å. |last5=Hansen |first5=Lars Kai |year=1999 |chapter=On Clustering fMRI Time Series |volume=9 |issue=3 |pages=298–310 |doi=10.1006/nimg.1998.0391 |pmid=10075900 |journal=NeuroImage |s2cid=14147564 |chapter-url=https://semanticscholar.org/paper/2d5c663fb53d8348bdf3c4df0f881b5db2dcf5e3 }}</ref><br /> * [[Dynamic Bayesian network]]<br /> * [[Time-frequency representation|Time-frequency analysis techniques:]]<br /> ** [[Fast Fourier transform]]<br /> ** [[Continuous wavelet transform]]<br /> ** [[Short-time Fourier transform]]<br /> ** [[Chirplet transform]]<br /> ** [[Fractional Fourier transform]]<br /> * [[Chaos theory|Chaotic analysis]]<br /> ** [[Correlation dimension]]<br /> ** [[Recurrence plot]]s<br /> ** [[Recurrence quantification analysis]]<br /> ** [[Lyapunov exponent]]s<br /> ** [[Entropy encoding]]<br /> <br /> * Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions)<br /> * Scaled cross- and auto-correlation functions to remove contributions of slow components<br /> * Performing a Fourier transform to investigate the series in the frequency domain<br /> * Use of a filter to remove unwanted noise<br /> * Principal component analysis (or empirical orthogonal function analysis)<br /> * Singular spectrum analysis<br /> * "Structural" models:<br /> ** General State Space Models<br /> ** Unobserved Components Models<br /> * Machine Learning<br /> ** Artificial neural networks<br /> ** Support vector machine<br /> ** Fuzzy logic<br /> ** Gaussian process<br /> ** Genetic Programming<br /> ** Gene expression programming<br /> ** Hidden Markov model<br /> ** Multi expression programming<br /> * Queueing theory analysis<br /> * Control chart<br /> ** Shewhart individuals control chart<br /> ** CUSUM chart<br /> ** EWMA chart<br /> * Detrended fluctuation analysis<br /> * Nonlinear mixed-effects modeling<br /> * Dynamic time warping<br /> * Cross-correlation<br /> * Dynamic Bayesian network<br /> * Time-frequency analysis techniques:<br /> ** Fast Fourier transform<br /> ** Continuous wavelet transform<br /> ** Short-time Fourier transform<br /> ** Chirplet transform<br /> ** Fractional Fourier transform<br /> * Chaotic analysis<br /> ** Correlation dimension<br /> ** Recurrence plots<br /> ** Recurrence quantification analysis<br /> ** Lyapunov exponents<br /> ** Entropy encoding<br /> <br /> <br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数) <br /> * 调整互相关函数和自相关函数以去除慢分量的贡献 <br /> * 在频域中执行一个傅里叶变换来调查这个序列 <br /> * 使用<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图 <br /> * <br /> * EWMA 图 <br /> * 非趋势波动分析 <br /> * 非线性混合效应建模 <br /> * <br /> * 动态时间规整互相关 <br /> * <br /> * 动态贝氏网路 <br /> * 时频分析技术: <br /> * <br /> * 快速傅里叶变换连续小波转换 <br /> * <br /> * 短时距傅里叶变换 <br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析 <br /> * <br /> * <br /> * 复发图 <br /> * <br /> * 递归量化分析 <br /> * <br /> * Lyapunov 指数 <br /> * <br /> * <br /> * <br /> * <br /> <br /> ===Measures===<br /> Time series metrics or [[Features (pattern recognition)|features]] that can be used for time series [[Classification (machine learning)|classification]] or [[regression analysis]]:<ref>{{cite journal |last1=Mormann |first1=Florian |last2=Andrzejak |first2=Ralph G. |last3=Elger |first3=Christian E. |last4=Lehnertz |first4=Klaus |title=Seizure prediction: the long and winding road |journal=[[Brain (journal)|Brain]] |year=2007 |volume=130 |issue=2 |pages=314–333 |doi=10.1093/brain/awl241 |pmid=17008335|doi-access=free }}</ref><br /> <br /> Time series metrics or features that can be used for time series classification or regression analysis:<br /> <br /> = = = = 可用于时间序列分类或回归分析的时间序列度量或特征:<br /> <br /> * '''Univariate linear measures'''<br /> ** [[Moment (mathematics)]]<br /> ** [[Spectral band power]]<br /> ** [[Spectral edge frequency]]<br /> ** Accumulated [[Energy (signal processing)]]<br /> ** Characteristics of the [[autocorrelation]] function<br /> ** [[Hjorth parameters]]<br /> ** [[Fast Fourier transform|FFT]] parameters<br /> ** [[Autoregressive model]] parameters<br /> ** [[Mann–Kendall test]]<br /> * '''Univariate non-linear measures'''<br /> ** Measures based on the [[correlation]] sum<br /> ** [[Correlation dimension]]<br /> ** [[Correlation integral]]<br /> ** [[Correlation density]]<br /> ** [[Correlation entropy]]<br /> ** [[Approximate entropy]]<ref>{{cite web |last1=Land |first1=Bruce |last2=Elias |first2=Damian |title=Measuring the 'Complexity' of a time series |url=http://www.nbb.cornell.edu/neurobio/land/PROJECTS/Complexity/ }}</ref><br /> ** [[Sample entropy]]<br /> ** {{iw2|Fourier entropy||uk|Ентропія Фур'є}}<br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** [[Rényi entropy]]<br /> ** Higher-order methods<br /> ** [[Marginal predictability]]<br /> ** [[Dynamical similarity]] index<br /> ** [[State space]] dissimilarity measures<br /> ** [[Lyapunov exponent]]<br /> ** Permutation methods<br /> ** [[Local flow]]<br /> * '''Other univariate measures'''<br /> ** [[Algorithmic information theory|Algorithmic complexity]]<br /> ** [[Kolmogorov complexity]] estimates<br /> ** [[Hidden Markov Model]] states<br /> ** [[Rough path#Signature|Rough path signature]]<ref>[1] Chevyrev, I., Kormilitzin, A. (2016) "[https://arxiv.org/abs/1603.03788 A Primer on the Signature Method in Machine Learning], arXiv:1603.03788v1"</ref><br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * '''Bivariate linear measures'''<br /> ** Maximum linear [[cross-correlation]]<br /> ** Linear [[Coherence (signal processing)]]<br /> * '''Bivariate non-linear measures'''<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for [[Phase synchronization]]<br /> ** Measures for [[Phase locking]]<br /> * '''Similarity measures''':<ref>{{cite journal |last1=Ropella |first1=G. E. P. |last2=Nag |first2=D. A. |last3=Hunt |first3=C. A. |title=Similarity measures for automated comparison of in silico and in vitro experimental results |journal=Engineering in Medicine and Biology Society |year=2003 |volume=3 |pages=2933–2936 |doi=10.1109/IEMBS.2003.1280532 |isbn=978-0-7803-7789-9 |s2cid=17798157 }}</ref><br /> ** [[Cross-correlation]]<br /> ** [[Dynamic Time Warping]]<ref name="Sakoe 1978"/><br /> ** [[Hidden Markov Models]]<br /> ** [[Edit distance]]<br /> ** [[Total correlation]]<br /> ** [[Newey–West estimator]]<br /> ** [[Prais–Winsten estimation|Prais–Winsten transformation]]<br /> ** Data as Vectors in a Metrizable Space<br /> *** [[Minkowski distance]]<br /> *** [[Mahalanobis distance]]<br /> ** Data as time series with envelopes<br /> *** Global [[standard deviation]]<br /> *** Local [[standard deviation]]<br /> *** Windowed [[standard deviation]]<br /> ** Data interpreted as stochastic series<br /> *** [[Pearson product-moment correlation coefficient]]<br /> *** [[Spearman's rank correlation coefficient]]<br /> ** Data interpreted as a [[probability distribution]] function<br /> *** [[Kolmogorov–Smirnov test]]<br /> *** [[Cramér–von Mises criterion]]<br /> <br /> * Univariate linear measures<br /> ** Moment (mathematics)<br /> ** Spectral band power<br /> ** Spectral edge frequency<br /> ** Accumulated Energy (signal processing)<br /> ** Characteristics of the autocorrelation function<br /> ** Hjorth parameters<br /> ** FFT parameters<br /> ** Autoregressive model parameters<br /> ** Mann–Kendall test<br /> * Univariate non-linear measures<br /> ** Measures based on the correlation sum<br /> ** Correlation dimension<br /> ** Correlation integral<br /> ** Correlation density<br /> ** Correlation entropy<br /> ** Approximate entropy<br /> ** Sample entropy<br /> ** <br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** Rényi entropy<br /> ** Higher-order methods<br /> ** Marginal predictability<br /> ** Dynamical similarity index<br /> ** State space dissimilarity measures<br /> ** Lyapunov exponent<br /> ** Permutation methods<br /> ** Local flow<br /> * Other univariate measures<br /> ** Algorithmic complexity<br /> ** Kolmogorov complexity estimates<br /> ** Hidden Markov Model states<br /> ** Rough path signature[1] Chevyrev, I., Kormilitzin, A. (2016) "A Primer on the Signature Method in Machine Learning, arXiv:1603.03788v1"<br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * Bivariate linear measures<br /> ** Maximum linear cross-correlation<br /> ** Linear Coherence (signal processing)<br /> * Bivariate non-linear measures<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for Phase synchronization<br /> ** Measures for Phase locking<br /> * Similarity measures:<br /> ** Cross-correlation<br /> ** Dynamic Time Warping<br /> ** Hidden Markov Models<br /> ** Edit distance<br /> ** Total correlation<br /> ** Newey–West estimator<br /> ** Prais–Winsten transformation<br /> ** Data as Vectors in a Metrizable Space<br /> *** Minkowski distance<br /> *** Mahalanobis distance<br /> ** Data as time series with envelopes<br /> *** Global standard deviation<br /> *** Local standard deviation<br /> *** Windowed standard deviation<br /> ** Data interpreted as stochastic series<br /> *** Pearson product-moment correlation coefficient<br /> *** Spearman's rank correlation coefficient<br /> ** Data interpreted as a probability distribution function<br /> *** Kolmogorov–Smirnov test<br /> *** Cramér–von Mises criterion<br /> <br /> <br /> * 单变量线性测量 <br /> * <br /> * 矩(数学) <br /> * <br /> * 谱带功率 <br /> * <br /> * 谱边缘频率 <br /> * <br /> * 累积能量(信号处理) <br /> * <br /> * 自相关函数特性 <br /> * <br /> * Hjorth 参数 <br /> * <br /> * FFT 参数 <br /> * <br /> * 自回归模型参数 <br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流 <br /> * 其他单变量度量 <br /> * <br /> * 算法复杂度 <br /> * <br /> * 柯氏复杂性估计 <br /> * <br /> * 隐马尔可夫模型状态 <br /> * <br /> * 粗糙路径签名[1] Chevyrev，i. ，Kormilitzin，a。(2016)“ a Primer on the Signature Method in Machine Learning，arXiv: 1603.03788 v1”<br /> * <br /> * 替代时间序列和替代校正 <br /> * <br /> * 递归损失(非平稳度) <br /> * 双变量线性度量 <br /> * <br /> * 最大线性互相关 <br /> * <br /> * 线性相干性(信号处理) <br /> * 双变量非线性度量 <br /> * <br /> * 非线性相互依赖 <br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学) <br /> * <br /> * 相位同步的度量 <br /> * <br /> * 相位锁定的度量 <br /> * <br /> * 相似度量: <br /> * <br /> * 互相关 <br /> * <br /> * <br /> * 动态时间规整 <br /> * <br /> * <br /> * 隐马尔可夫模型 <br /> * <br /> * <br /> * 编辑距离 <br /> * <br /> * 总相关性 <br /> * <br /> * Newey-West 估计 <br /> * <br /> * Prais-Winsten 变换 <br /> * <br /> * 数据作为向量在乌雷松度量化定理 <br /> * <br /> * <br /> * 明氏距离 <br /> * <br /> * 马氏距离 <br /> * <br /> * 数据作为时间序列与信封 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差标准差 <br /> * <br /> * <br /> * 窗口标准差 <br /> * <br /> * 数据解释为随机序列 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数 <br /> * <br /> * 数据解释为概率分布函数 <br /> * <br /> * Kolmogorov-Smirnov 检验 <br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ==Visualization==<br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<ref>{{cite web|last1=Tominski|first1=Christian|last2= Aigner|first2=Wolfgang|title=The TimeViz Browser:A Visual Survey of Visualization Techniques for Time-Oriented Data|url=http://survey.timeviz.net/|access-date=1 June 2014}}</ref><br /> <br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<br /> <br /> = = 可视化 = = 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> ===Overlapping charts===<br /> * [[Braided graphs]]<br /> * Line charts<br /> * Slope graphs<br /> * {{iw2|GapChart||fr}}<br /> <br /> * Braided graphs<br /> * Line charts<br /> * Slope graphs<br /> * <br /> <br /> = = = = 重叠图 = = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> ===Separated charts===<br /> * [[Horizon graphs]]<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> * Horizon graphs<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> = = = = = 分离图表 = = = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ==See also==<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ==References==<br /> {{Reflist|2}}<br /> <br /> ==Further reading==<br /> * {{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> * [[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> * {{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> * {{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> * [[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]]. {{ISBN|978-0-12-564901-8}}<br /> * {{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer, {{ISBN|978-3-319-52451-1}}<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> * [[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> * {{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> = = 进一步阅读 = = <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社。<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社。<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去。北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社。<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社。<br /> *<br /> <br /> ==External links==<br /> {{Commons category}}<br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> <br /> *Introduction to Time series Analysis (Engineering Statistics Handbook) — A practical guide to Time series analysis.<br /> <br /> = = 外部链接 = = <br /> * 时间序列分析导论(工程统计手册)ー时间序列分析实用指南。<br /> <br /> {{Statistics}}<br /> {{Portal bar|Mathematics}}<br /> {{Authority control}}<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> <br /> <br /> <br /> Category:Statistical data types<br /> Category:Mathematical and quantitative methods (economics)<br /> Category:Machine learning<br /> <br /> 类别: 统计数据类型类别: 数学和定量方法(经济学)类别: 机器学习<br /> <br /> <noinclude><br /> <br /> <small>This page was moved from [[wikipedia:en:Time series]]. Its edit history can be viewed at [[时间序列分析/edithistory]]</small></noinclude><br /> <br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33947 时间序列分析 2023-02-05T09:20:15Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数值Numeric数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ==分析方法==<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些方法中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ==面板数据==<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==分析==<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> 其他技巧包括:<br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> 曲线拟合<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> 是构建一条曲线或数学函数的过程，它对一系列的数据点具有最佳的拟合效果<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref>，但也可能会受到一些限制<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref>。曲线拟合包括插值<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref>（需要精确地拟合数据）与平滑<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref>（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref>更侧重于统计推断的问题。例如，在拟合有随机误差的数据的曲线中，推测有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref>，在没有数据的情况下推断函数的值<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref>，并总结两个或多个变量之间的关系<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref>。外推法是指在观测到的数据范围之外使用拟合曲线<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref>，它有一定程度的不确定性<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref>，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的基准值之间进行插值来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref>。如果与缺失数据相关的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref>。或者使用多项式插值或样条插值，将分段多项式函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> <br /> 外推法是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值I类似，插值在已知的观测值之间产生估计值，但外推法的不确定性更大，产生无意义结果的风险也更大。<br /> <br /> ===函数逼近问题===<br /> {{main|Function approximation}}<br /> <br /> <br /> 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配。对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(连续性、积分和极限值等等)。<br /> <br /> <br /> 时间序列分析的目标函数，例如 g，可能是未知的。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。<br /> <br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===时间序列分析的预测功能===<br /> In [[statistics]], [[prediction]] is a part of [[statistical inference]]. One particular approach to such inference is known as [[predictive inference]], but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as [[forecasting]].<br /> * Fully formed statistical models for [[stochastic simulation]] purposes, so as to generate alternative versions of the time series, representing what might happen over non-specific time-periods in the future<br /> * Simple or fully formed statistical models to describe the likely outcome of the time series in the immediate future, given knowledge of the most recent outcomes (forecasting).<br /> * Forecasting on time series is usually done using automated statistical software packages and programming languages, such as [[Julia (programming language)|Julia]], [[Python (programming language)|Python]], [[R (programming language)|R]], [[SAS (software)|SAS]], [[SPSS]] and many others.<br /> * Forecasting on large scale data can be done with [[Apache Spark]] using the Spark-TS library, a third-party package.<ref>{{cite web |title=Time Series Analysis with Spark |author=Sandy Ryza |date=2020-03-18 |access-date=2021-01-12 |url=https://databricks.com/session/time-series-analysis-with-spark |format=slides of a talk at Spark Summit East 2016 |publisher=[[Databricks]]}}</ref><br /> <br /> In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as forecasting.<br /> * Fully formed statistical models for stochastic simulation purposes, so as to generate alternative versions of the time series, representing what might happen over non-specific time-periods in the future<br /> * Simple or fully formed statistical models to describe the likely outcome of the time series in the immediate future, given knowledge of the most recent outcomes (forecasting).<br /> * Forecasting on time series is usually done using automated statistical software packages and programming languages, such as Julia, Python, R, SAS, SPSS and many others.<br /> * Forecasting on large scale data can be done with Apache Spark using the Spark-TS library, a third-party package.<br /> <br /> 在统计学中，预测是推论统计学的一部分。一种特殊的推理方法被称为预测推理，但是这种预测可以在几种推论统计学推理方法中的任何一种中进行。事实上，对统计的一种描述是，它提供了一种将关于某一人口样本的知识转移给整个人口和其他相关人口的手段，这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，这个过程就被称为预测。<br /> * 为随机模拟目的而建立完整的统计模型，以产生时间序列的替代版本，反映未来在非特定时间段内可能发生的情况 <br /> * 简单或完整的统计模型，以描述时间序列在最近期间可能产生的结果(预测)。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===Classification===<br /> {{main|Statistical classification}}<br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in [[sign language]].<br /> <br /> <br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in sign language.<br /> <br /> = = = 分类 = = 将时间序列模式分配到一个特定的类别，例如根据手语中的一系列动作识别一个单词。<br /> <br /> ===Signal estimation===<br /> {{see also|Signal processing|Estimation theory}}<br /> This approach is based on [[harmonic analysis]] and filtering of signals in the [[frequency domain]] using the [[Fourier transform]], and [[spectral density estimation]], the development of which was significantly accelerated during [[World War II]] by mathematician [[Norbert Wiener]], electrical engineers [[Rudolf E. Kálmán]], [[Dennis Gabor]] and others for filtering signals from noise and predicting signal values at a certain point in time. See [[Kalman filter]], [[Estimation theory]], and [[Digital signal processing]]<br /> <br /> <br /> This approach is based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation, the development of which was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. See Kalman filter, Estimation theory, and Digital signal processing<br /> <br /> = = = 信号估计 = = = 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，其发展是显着加速二战期间由数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯 Gabor 和其他人从噪音信号过滤和预测信号值在一定时间点。参见卡尔曼滤波器，参数估测和数字信号处理<br /> <br /> ===Segmentation===<br /> {{main|Time-series segmentation}}<br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using [[Change detection|change-point detection]], or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> <br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using change-point detection, or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> = = = 分割 = = 将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。在时间序列分割中，目标是识别时间序列中的分段边界点，并刻画每个分段的动态特性。人们可以通过变点检测来解决这个问题，或者将时间序列建模为一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ==Models==<br /> <br /> ==Models==<br /> <br /> = = 模型 = = <br /> <br /> Models for time series data can have many forms and represent different [[stochastic processes]]. When modeling variations in the level of a process, three broad classes of practical importance are the ''[[autoregressive]]'' (AR) models, the ''integrated'' (I) models, and the ''[[moving average model|moving average]]'' (MA) models. These three classes depend linearly on previous data points.<ref name="linear time series">{{cite book |author-link=Neil Gershenfeld |last=Gershenfeld |first=N. |year=1999 |title=The Nature of Mathematical Modeling |url=https://archive.org/details/naturemathematic00gers_334 |url-access=limited |location=New York |publisher=Cambridge University Press |pages=[https://archive.org/details/naturemathematic00gers_334/page/n206 205]–208 |isbn=978-0521570954 }}</ref> Combinations of these ideas produce [[autoregressive moving average]] (ARMA) and [[autoregressive integrated moving average]] (ARIMA) models. The [[autoregressive fractionally integrated moving average]] (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for [[vector autoregression]]. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> Models for time series data can have many forms and represent different stochastic processes. When modeling variations in the level of a process, three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. These three classes depend linearly on previous data points. Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models. The autoregressive fractionally integrated moving average (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector autoregression. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> 时间序列数据的模型可以有多种形式，表示不同的随机过程。在对过程层次的变化进行建模时，三大类实际的重要性是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个类线性地依赖于以前的数据点。这些想法的结合产生了自回归移动平均(ARMA)和 ARIMA模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对前三种模型进行了推广。处理矢量值数据的这些类的扩展可以在多元时间序列模型的标题下得到，有时前面的首字母缩略词被扩展，包括一个初始的“ v”代表“矢量”，如在 VAR 代表向量自回归模型。这些模型的另外一组扩展可用于观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应) : 与多变量情况的区别在于强迫序列可能是确定的或者在实验者的控制之下。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a [[chaos theory|chaotic]] time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in [[nonlinear autoregressive exogenous model]]s. Further references on nonlinear time series analysis: (Kantz and Schreiber),<ref>{{cite book|last1=Kantz|first1=Holger|last2=Thomas|first2=Schreiber|title=Nonlinear Time Series Analysis|date=2004|publisher=Cambridge University Press|location=London|isbn=978-0521529020}}</ref> and (Abarbanel)<ref>{{cite book|last1=Abarbanel|first1=Henry|title=Analysis of Observed Chaotic Data|date=Nov 25, 1997|publisher=Springer|location=New York|isbn=978-0387983721}}</ref><br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a chaotic time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in nonlinear autoregressive exogenous models. Further references on nonlinear time series analysis: (Kantz and Schreiber), and (Abarbanel)<br /> <br /> 一系列数据的水平对以前的数据点的非线性依赖是有趣的，部分是因为产生混沌时间序列的可能性。然而，更重要的是，经验调查可以表明使用来自非线性模型的预测优于来自线性模型的预测，例如在非线性自回归外生模型中。非线性时间序列分析的进一步参考文献: (Kantz 和 Schreiber)和(Abarbanel) <br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time ([[heteroskedasticity]]). These models represent [[autoregressive conditional heteroskedasticity]] (ARCH) and the collection comprises a wide variety of representation ([[GARCH]], TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a [[doubly stochastic model]].<br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time (heteroskedasticity). These models represent autoregressive conditional heteroskedasticity (ARCH) and the collection comprises a wide variety of representation (GARCH, TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a doubly stochastic model.<br /> <br /> 在其他类型的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型代表了 ARCH模型(ARCH) ，收藏包括各种各样的代表(GARCH，TARCH，EGARCH，FIGARCH，CGARCH 等等)。在这里，变异性的变化与观测系列的最近过去的值有关，或者是预测的。这与局部变化的其他可能表现形式形成对比，在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also [[Markov switching multifractal]] (MSMF) techniques for modeling volatility evolution.<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution.<br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列，试图说明在多个尺度上的时间依赖。参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> A [[Hidden Markov model]] (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest [[dynamic Bayesian network]]. HMM models are widely used in [[speech recognition]], for translating a time series of spoken words into text.<br /> <br /> A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.<br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔科姆可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，用于将语音序列转换成文本。<br /> <br /> ===Notation===<br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series ''X'' that is indexed by the [[natural number]]s is written<br /> :''X'' = (''X''<sub>1</sub>, ''X''<sub>2</sub>, ...).<br /> <br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written<br /> :X = (X1, X2, ...).<br /> <br /> = = = 表示法 = = 用于时间序列分析的许多不同的表示法。一个用于指定时间序列 x 的通用符号是: x = (X1，X2，...)。<br /> <br /> Another common notation is<br /> :''Y'' = (''Y<sub>t</sub>'': ''t'' ∈ ''T''),<br /> where ''T'' is the [[index set]].<br /> <br /> Another common notation is<br /> :Y = (Yt: t ∈ T),<br /> where T is the index set.<br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===Conditions===<br /> There are two sets of conditions under which much of the theory is built:<br /> * [[Stationary process]]<br /> * [[Ergodic process]]<br /> <br /> There are two sets of conditions under which much of the theory is built:<br /> * Stationary process<br /> * Ergodic process<br /> <br /> 这个理论的大部分建立在两个条件之下: <br /> * 平稳过程遍历过程<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: [[strict stationarity]] and [[Stationary process#Weaker forms of stationarity|second-order stationarity]]. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: strict stationarity and second-order stationarity. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> 然而，平稳性的概念必须扩展到考虑两个重要的概念: 严格平稳性和二阶平稳性。模型和应用程序都可以在这些条件中的每一种情况下开发，尽管后一种情况下的模型可能被认为只是部分具体说明。<br /> <br /> In addition, time-series analysis can be applied where the series are [[Cyclostationary process|seasonally stationary]] or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in [[time-frequency analysis]] which makes use of a [[time–frequency representation]] of a time-series or signal.<ref>Boashash, B. (ed.), (2003) ''Time-Frequency Signal Analysis and Processing: A Comprehensive Reference'', Elsevier Science, Oxford, 2003 {{isbn|0-08-044335-4}}</ref><br /> <br /> In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.Boashash, B. (ed.), (2003) Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003 <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或非平稳的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。波阿什，b。我不知道你在说什么。) ，(2003)《时频信号分析与处理: 综合参考》，爱思唯尔科学出版社，牛津，2003<br /> <br /> ===Tools===<br /> Tools for investigating time-series data include:<br /> <br /> Tools for investigating time-series data include:<br /> <br /> = = = 调查时间序列数据的工具包括:<br /> <br /> * Consideration of the [[autocorrelation|autocorrelation function]] and the [[Spectral density|spectral density function]] (also [[cross-correlation function]]s and cross-spectral density functions)<br /> * [[Scaled correlation|Scaled]] cross- and auto-correlation functions to remove contributions of slow components<ref name="Nikolicetal">{{cite journal |last1=Nikolić |first1=D. |last2=Muresan |first2=R. C. |last3=Feng |first3=W. |last4=Singer |first4=W. |year=2012 |title=Scaled correlation analysis: a better way to compute a cross-correlogram |journal=European Journal of Neuroscience |volume=35 |issue=5 |pages=742–762 |doi=10.1111/j.1460-9568.2011.07987.x |pmid=22324876 |s2cid=4694570 |url=https://semanticscholar.org/paper/caa784fc3c22656413143559c402b54d0567f4d1 }}</ref><br /> * Performing a [[Fourier transform]] to investigate the series in the [[frequency domain]]<br /> * Use of a [[digital filter|filter]] to remove unwanted [[noise (physics)|noise]]<br /> * [[Principal component analysis]] (or [[empirical orthogonal function]] analysis)<br /> * [[Singular spectrum analysis]]<br /> * "Structural" models:<br /> ** General [[State Space Model]]s<br /> ** Unobserved Components Models<br /> * [[Machine Learning]]<br /> ** [[Artificial neural network]]s<br /> ** [[Support vector machine]]<br /> ** [[Fuzzy logic]]<br /> ** [[Gaussian process]]<br /> ** [[Genetic Programming]]<br /> ** [[Gene expression programming]]<br /> ** [[Hidden Markov model]]<br /> ** [[Multi expression programming]]<br /> * [[Queueing theory]] analysis<br /> * [[Control chart]]<br /> ** [[Shewhart individuals control chart]]<br /> ** [[CUSUM]] chart<br /> ** [[EWMA chart]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Nonlinear mixed-effects model|Nonlinear mixed-effects modeling]]<br /> * [[Dynamic time warping]]<ref name="Sakoe 1978">{{cite book |last1=Sakoe |first1=Hiroaki |last2=Chiba |first2=Seibi |year=1978 |chapter=Dynamic programming algorithm optimization for spoken word recognition |volume=26 |pages=43–49 |doi=10.1109/TASSP.1978.1163055 |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |s2cid=17900407 |chapter-url=https://semanticscholar.org/paper/18f355d7ef4aa9f82bf5c00f84e46714efa5fd77 }}</ref><br /> * [[Cross-correlation]]<ref>{{cite book |last1=Goutte |first1=Cyril |last2=Toft |first2=Peter |last3=Rostrup |first3=Egill |last4=Nielsen |first4=Finn Å. |last5=Hansen |first5=Lars Kai |year=1999 |chapter=On Clustering fMRI Time Series |volume=9 |issue=3 |pages=298–310 |doi=10.1006/nimg.1998.0391 |pmid=10075900 |journal=NeuroImage |s2cid=14147564 |chapter-url=https://semanticscholar.org/paper/2d5c663fb53d8348bdf3c4df0f881b5db2dcf5e3 }}</ref><br /> * [[Dynamic Bayesian network]]<br /> * [[Time-frequency representation|Time-frequency analysis techniques:]]<br /> ** [[Fast Fourier transform]]<br /> ** [[Continuous wavelet transform]]<br /> ** [[Short-time Fourier transform]]<br /> ** [[Chirplet transform]]<br /> ** [[Fractional Fourier transform]]<br /> * [[Chaos theory|Chaotic analysis]]<br /> ** [[Correlation dimension]]<br /> ** [[Recurrence plot]]s<br /> ** [[Recurrence quantification analysis]]<br /> ** [[Lyapunov exponent]]s<br /> ** [[Entropy encoding]]<br /> <br /> * Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions)<br /> * Scaled cross- and auto-correlation functions to remove contributions of slow components<br /> * Performing a Fourier transform to investigate the series in the frequency domain<br /> * Use of a filter to remove unwanted noise<br /> * Principal component analysis (or empirical orthogonal function analysis)<br /> * Singular spectrum analysis<br /> * "Structural" models:<br /> ** General State Space Models<br /> ** Unobserved Components Models<br /> * Machine Learning<br /> ** Artificial neural networks<br /> ** Support vector machine<br /> ** Fuzzy logic<br /> ** Gaussian process<br /> ** Genetic Programming<br /> ** Gene expression programming<br /> ** Hidden Markov model<br /> ** Multi expression programming<br /> * Queueing theory analysis<br /> * Control chart<br /> ** Shewhart individuals control chart<br /> ** CUSUM chart<br /> ** EWMA chart<br /> * Detrended fluctuation analysis<br /> * Nonlinear mixed-effects modeling<br /> * Dynamic time warping<br /> * Cross-correlation<br /> * Dynamic Bayesian network<br /> * Time-frequency analysis techniques:<br /> ** Fast Fourier transform<br /> ** Continuous wavelet transform<br /> ** Short-time Fourier transform<br /> ** Chirplet transform<br /> ** Fractional Fourier transform<br /> * Chaotic analysis<br /> ** Correlation dimension<br /> ** Recurrence plots<br /> ** Recurrence quantification analysis<br /> ** Lyapunov exponents<br /> ** Entropy encoding<br /> <br /> <br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数) <br /> * 调整互相关函数和自相关函数以去除慢分量的贡献 <br /> * 在频域中执行一个傅里叶变换来调查这个序列 <br /> * 使用<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图 <br /> * <br /> * EWMA 图 <br /> * 非趋势波动分析 <br /> * 非线性混合效应建模 <br /> * <br /> * 动态时间规整互相关 <br /> * <br /> * 动态贝氏网路 <br /> * 时频分析技术: <br /> * <br /> * 快速傅里叶变换连续小波转换 <br /> * <br /> * 短时距傅里叶变换 <br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析 <br /> * <br /> * <br /> * 复发图 <br /> * <br /> * 递归量化分析 <br /> * <br /> * Lyapunov 指数 <br /> * <br /> * <br /> * <br /> * <br /> <br /> ===Measures===<br /> Time series metrics or [[Features (pattern recognition)|features]] that can be used for time series [[Classification (machine learning)|classification]] or [[regression analysis]]:<ref>{{cite journal |last1=Mormann |first1=Florian |last2=Andrzejak |first2=Ralph G. |last3=Elger |first3=Christian E. |last4=Lehnertz |first4=Klaus |title=Seizure prediction: the long and winding road |journal=[[Brain (journal)|Brain]] |year=2007 |volume=130 |issue=2 |pages=314–333 |doi=10.1093/brain/awl241 |pmid=17008335|doi-access=free }}</ref><br /> <br /> Time series metrics or features that can be used for time series classification or regression analysis:<br /> <br /> = = = = 可用于时间序列分类或回归分析的时间序列度量或特征:<br /> <br /> * '''Univariate linear measures'''<br /> ** [[Moment (mathematics)]]<br /> ** [[Spectral band power]]<br /> ** [[Spectral edge frequency]]<br /> ** Accumulated [[Energy (signal processing)]]<br /> ** Characteristics of the [[autocorrelation]] function<br /> ** [[Hjorth parameters]]<br /> ** [[Fast Fourier transform|FFT]] parameters<br /> ** [[Autoregressive model]] parameters<br /> ** [[Mann–Kendall test]]<br /> * '''Univariate non-linear measures'''<br /> ** Measures based on the [[correlation]] sum<br /> ** [[Correlation dimension]]<br /> ** [[Correlation integral]]<br /> ** [[Correlation density]]<br /> ** [[Correlation entropy]]<br /> ** [[Approximate entropy]]<ref>{{cite web |last1=Land |first1=Bruce |last2=Elias |first2=Damian |title=Measuring the 'Complexity' of a time series |url=http://www.nbb.cornell.edu/neurobio/land/PROJECTS/Complexity/ }}</ref><br /> ** [[Sample entropy]]<br /> ** {{iw2|Fourier entropy||uk|Ентропія Фур'є}}<br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** [[Rényi entropy]]<br /> ** Higher-order methods<br /> ** [[Marginal predictability]]<br /> ** [[Dynamical similarity]] index<br /> ** [[State space]] dissimilarity measures<br /> ** [[Lyapunov exponent]]<br /> ** Permutation methods<br /> ** [[Local flow]]<br /> * '''Other univariate measures'''<br /> ** [[Algorithmic information theory|Algorithmic complexity]]<br /> ** [[Kolmogorov complexity]] estimates<br /> ** [[Hidden Markov Model]] states<br /> ** [[Rough path#Signature|Rough path signature]]<ref>[1] Chevyrev, I., Kormilitzin, A. (2016) "[https://arxiv.org/abs/1603.03788 A Primer on the Signature Method in Machine Learning], arXiv:1603.03788v1"</ref><br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * '''Bivariate linear measures'''<br /> ** Maximum linear [[cross-correlation]]<br /> ** Linear [[Coherence (signal processing)]]<br /> * '''Bivariate non-linear measures'''<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for [[Phase synchronization]]<br /> ** Measures for [[Phase locking]]<br /> * '''Similarity measures''':<ref>{{cite journal |last1=Ropella |first1=G. E. P. |last2=Nag |first2=D. A. |last3=Hunt |first3=C. A. |title=Similarity measures for automated comparison of in silico and in vitro experimental results |journal=Engineering in Medicine and Biology Society |year=2003 |volume=3 |pages=2933–2936 |doi=10.1109/IEMBS.2003.1280532 |isbn=978-0-7803-7789-9 |s2cid=17798157 }}</ref><br /> ** [[Cross-correlation]]<br /> ** [[Dynamic Time Warping]]<ref name="Sakoe 1978"/><br /> ** [[Hidden Markov Models]]<br /> ** [[Edit distance]]<br /> ** [[Total correlation]]<br /> ** [[Newey–West estimator]]<br /> ** [[Prais–Winsten estimation|Prais–Winsten transformation]]<br /> ** Data as Vectors in a Metrizable Space<br /> *** [[Minkowski distance]]<br /> *** [[Mahalanobis distance]]<br /> ** Data as time series with envelopes<br /> *** Global [[standard deviation]]<br /> *** Local [[standard deviation]]<br /> *** Windowed [[standard deviation]]<br /> ** Data interpreted as stochastic series<br /> *** [[Pearson product-moment correlation coefficient]]<br /> *** [[Spearman's rank correlation coefficient]]<br /> ** Data interpreted as a [[probability distribution]] function<br /> *** [[Kolmogorov–Smirnov test]]<br /> *** [[Cramér–von Mises criterion]]<br /> <br /> * Univariate linear measures<br /> ** Moment (mathematics)<br /> ** Spectral band power<br /> ** Spectral edge frequency<br /> ** Accumulated Energy (signal processing)<br /> ** Characteristics of the autocorrelation function<br /> ** Hjorth parameters<br /> ** FFT parameters<br /> ** Autoregressive model parameters<br /> ** Mann–Kendall test<br /> * Univariate non-linear measures<br /> ** Measures based on the correlation sum<br /> ** Correlation dimension<br /> ** Correlation integral<br /> ** Correlation density<br /> ** Correlation entropy<br /> ** Approximate entropy<br /> ** Sample entropy<br /> ** <br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** Rényi entropy<br /> ** Higher-order methods<br /> ** Marginal predictability<br /> ** Dynamical similarity index<br /> ** State space dissimilarity measures<br /> ** Lyapunov exponent<br /> ** Permutation methods<br /> ** Local flow<br /> * Other univariate measures<br /> ** Algorithmic complexity<br /> ** Kolmogorov complexity estimates<br /> ** Hidden Markov Model states<br /> ** Rough path signature[1] Chevyrev, I., Kormilitzin, A. (2016) "A Primer on the Signature Method in Machine Learning, arXiv:1603.03788v1"<br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * Bivariate linear measures<br /> ** Maximum linear cross-correlation<br /> ** Linear Coherence (signal processing)<br /> * Bivariate non-linear measures<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for Phase synchronization<br /> ** Measures for Phase locking<br /> * Similarity measures:<br /> ** Cross-correlation<br /> ** Dynamic Time Warping<br /> ** Hidden Markov Models<br /> ** Edit distance<br /> ** Total correlation<br /> ** Newey–West estimator<br /> ** Prais–Winsten transformation<br /> ** Data as Vectors in a Metrizable Space<br /> *** Minkowski distance<br /> *** Mahalanobis distance<br /> ** Data as time series with envelopes<br /> *** Global standard deviation<br /> *** Local standard deviation<br /> *** Windowed standard deviation<br /> ** Data interpreted as stochastic series<br /> *** Pearson product-moment correlation coefficient<br /> *** Spearman's rank correlation coefficient<br /> ** Data interpreted as a probability distribution function<br /> *** Kolmogorov–Smirnov test<br /> *** Cramér–von Mises criterion<br /> <br /> <br /> * 单变量线性测量 <br /> * <br /> * 矩(数学) <br /> * <br /> * 谱带功率 <br /> * <br /> * 谱边缘频率 <br /> * <br /> * 累积能量(信号处理) <br /> * <br /> * 自相关函数特性 <br /> * <br /> * Hjorth 参数 <br /> * <br /> * FFT 参数 <br /> * <br /> * 自回归模型参数 <br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流 <br /> * 其他单变量度量 <br /> * <br /> * 算法复杂度 <br /> * <br /> * 柯氏复杂性估计 <br /> * <br /> * 隐马尔可夫模型状态 <br /> * <br /> * 粗糙路径签名[1] Chevyrev，i. ，Kormilitzin，a。(2016)“ a Primer on the Signature Method in Machine Learning，arXiv: 1603.03788 v1”<br /> * <br /> * 替代时间序列和替代校正 <br /> * <br /> * 递归损失(非平稳度) <br /> * 双变量线性度量 <br /> * <br /> * 最大线性互相关 <br /> * <br /> * 线性相干性(信号处理) <br /> * 双变量非线性度量 <br /> * <br /> * 非线性相互依赖 <br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学) <br /> * <br /> * 相位同步的度量 <br /> * <br /> * 相位锁定的度量 <br /> * <br /> * 相似度量: <br /> * <br /> * 互相关 <br /> * <br /> * <br /> * 动态时间规整 <br /> * <br /> * <br /> * 隐马尔可夫模型 <br /> * <br /> * <br /> * 编辑距离 <br /> * <br /> * 总相关性 <br /> * <br /> * Newey-West 估计 <br /> * <br /> * Prais-Winsten 变换 <br /> * <br /> * 数据作为向量在乌雷松度量化定理 <br /> * <br /> * <br /> * 明氏距离 <br /> * <br /> * 马氏距离 <br /> * <br /> * 数据作为时间序列与信封 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差标准差 <br /> * <br /> * <br /> * 窗口标准差 <br /> * <br /> * 数据解释为随机序列 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数 <br /> * <br /> * 数据解释为概率分布函数 <br /> * <br /> * Kolmogorov-Smirnov 检验 <br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ==Visualization==<br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<ref>{{cite web|last1=Tominski|first1=Christian|last2= Aigner|first2=Wolfgang|title=The TimeViz Browser:A Visual Survey of Visualization Techniques for Time-Oriented Data|url=http://survey.timeviz.net/|access-date=1 June 2014}}</ref><br /> <br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<br /> <br /> = = 可视化 = = 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> ===Overlapping charts===<br /> * [[Braided graphs]]<br /> * Line charts<br /> * Slope graphs<br /> * {{iw2|GapChart||fr}}<br /> <br /> * Braided graphs<br /> * Line charts<br /> * Slope graphs<br /> * <br /> <br /> = = = = 重叠图 = = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> ===Separated charts===<br /> * [[Horizon graphs]]<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> * Horizon graphs<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> = = = = = 分离图表 = = = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ==See also==<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ==References==<br /> {{Reflist|2}}<br /> <br /> ==Further reading==<br /> * {{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> * [[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> * {{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> * {{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> * [[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]]. {{ISBN|978-0-12-564901-8}}<br /> * {{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer, {{ISBN|978-3-319-52451-1}}<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> * [[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> * {{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> = = 进一步阅读 = = <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社。<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社。<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去。北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社。<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社。<br /> *<br /> <br /> ==External links==<br /> {{Commons category}}<br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> <br /> *Introduction to Time series Analysis (Engineering Statistics Handbook) — A practical guide to Time series analysis.<br /> <br /> = = 外部链接 = = <br /> * 时间序列分析导论(工程统计手册)ー时间序列分析实用指南。<br /> <br /> {{Statistics}}<br /> {{Portal bar|Mathematics}}<br /> {{Authority control}}<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> <br /> <br /> <br /> Category:Statistical data types<br /> Category:Mathematical and quantitative methods (economics)<br /> Category:Machine learning<br /> <br /> 类别: 统计数据类型类别: 数学和定量方法(经济学)类别: 机器学习<br /> <br /> <noinclude><br /> <br /> <small>This page was moved from [[wikipedia:en:Time series]]. Its edit history can be viewed at [[时间序列分析/edithistory]]</small></noinclude><br /> <br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33946 时间序列分析 2023-02-05T04:25:50Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数值Numeric数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ==分析方法==<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些方法中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> ==面板数据==<br /> <br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断是面板数据还是时间序列的方法之一是探究使一条数据记录与其他记录不同的因素。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==Analysis分析==<br /> <br /> <br /> 不同目的的时间序列适用的动机和数据分析方法都不同。<br /> <br /> ===动机===<br /> <br /> <br /> 在统计学、计量经济学、定量金融、地震学、气象学和地球物理学方面，时间序列分析的主要目标是预测。在信号处理、控制工程和通信工程方面，它被用于信号检测。在数据挖掘、模式识别和机器学习等其他应用中，时间序列分析可用于聚类、分类、按内容查询<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref>、异常检测以及预测。<br /> <br /> ===探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> <br /> <br /> 绘制折线图是分析常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，且在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，可以在一个图表中比较两个时间序列。<br /> <br /> <br /> <br /> <br /> <br /> 一项对企业数据分析师的研究发现，探索性时间的序列分析有两个挑战：发现新模式，以及为这些模式找到解释<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref>。将时间序列数据可视化为热力图矩阵的工具可以帮助解释这些模式。<br /> <br /> <br /> <br /> <br /> <br /> 其他技巧包括:<br /> <br /> * 通过自相关分析去检验序列相关性；<br /> * 通过频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。周期性行为常见的例子也包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分；<br /> <br /> ===曲线拟合===<br /> {{main|Curve fitting}}<br /> <br /> Curve fitting<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> is the process of constructing a [[curve]], or [[function (mathematics)|mathematical function]], that has the best fit to a series of [[data]] points,<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref> possibly subject to constraints.<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref> Curve fitting can involve either [[interpolation]],<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref> where an exact fit to the data is required, or [[smoothing]],<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref> in which a "smooth" function is constructed that approximately fits the data. A related topic is [[regression analysis]],<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref> which focuses more on questions of [[statistical inference]] such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization,<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref> to infer values of a function where no data are available,<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref> and to summarize the relationships among two or more variables.<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref> [[Extrapolation]] refers to the use of a fitted curve beyond the [[range (statistics)|range]] of the observed data,<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref> and is subject to a [[Uncertainty|degree of uncertainty]]<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref> since it may reflect the method used to construct the curve as much as it reflects the observed data.<br /> <br /> 正文：曲线拟合Curve fitting<br /> <br /> 曲线拟合<ref name=":7" /><ref name=":8" /> 是构建一条曲线Curve或数学函数Mathematical function的过程，它对一系列的数据Data点具有最佳的拟合效果<ref name=":9" />，可能会受到一些限制<ref name=":10" /><ref name=":11" />。曲线拟合包括插值Interpolation<ref name=":12" /><ref name=":13" />（需要精确地拟合数据）与平滑Smoothing<ref name=":14" /><ref name=":15" />（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析Regression analysis<ref name=":16" /><ref name=":17" />更侧重于统计推断Statistical inference的问题。例如，在拟合有随机误差的数据的曲线中，有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18" /><ref name=":19" />，在没有数据的情况下推断函数的值<ref name=":20" />，并总结两个或多个变量之间的关系<ref name=":21" />。外推法Extrapolation是指在观测到的数据范围Range之外使用拟合曲线<ref name=":22" />，它有一定程度的不确定性Degree of uncertainty<ref name=":23" />，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> <br /> The construction of economic time series involves the estimation of some components for some dates by [[interpolation]] between values ("benchmarks") for earlier and later dates. Interpolation is estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from the available information ("reading between the lines").<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref> Interpolation is useful where the data surrounding the missing data is available and its trend, seasonality, and longer-term cycles are known. This is often done by using a related series known for all relevant dates.<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref> Alternatively [[polynomial interpolation]] or [[spline interpolation]] is used where piecewise [[polynomial]] functions are fit into time intervals such that they fit smoothly together. A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function (also called [[Polynomial regression|regression]]).The main difference between regression and interpolation is that polynomial regression gives a single polynomial that models the entire data set. Spline interpolation, however, yield a piecewise continuous function composed of many polynomials to model the data set.<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的值（“基准”）之间进行插值Interpolation来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24" />。如果围绕缺失数据的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25" />。或者使用多项式插值Polynomial interpolation或样条插值Spline interpolation，将分段多项式Polynomial函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归Regression）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而样条插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> [[Extrapolation]] is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable. It is similar to [[interpolation]], which produces estimates between known observations, but extrapolation is subject to greater [[uncertainty]] and a higher risk of producing meaningless results.<br /> <br /> 外推法Extrapolation是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值Interpolation类似，插值在已知的观测值之间产生估计值，但外推法的不确定性Uncertainty更大，产生无意义结果的风险也更大。<br /> <br /> ===Function approximation===<br /> {{main|Function approximation}}<br /> In general, a function approximation problem asks us to select a [[function (mathematics)|function]] among a well-defined class that closely matches ("approximates") a target function in a task-specific way.<br /> One can distinguish two major classes of function approximation problems: First, for known target functions, [[approximation theory]] is the branch of [[numerical analysis]] that investigates how certain known functions (for example, [[special function]]s) can be approximated by a specific class of functions (for example, [[polynomial]]s or [[rational function]]s) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).<br /> <br /> <br /> In general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way.<br /> One can distinguish two major classes of function approximation problems: First, for known target functions, approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions) can be approximated by a specific class of functions (for example, polynomials or rational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).<br /> <br /> = = = = = = = = 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配(“近似”)。人们可以区分两类主要的函数逼近问题: 首先，对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数(例如，特殊函数)如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(廉价计算、连续性、积分和极限值等等)。).<br /> <br /> Second, the target function, call it ''g'', may be unknown; instead of an explicit formula, only a set of points (a time series) of the form (''x'', ''g''(''x'')) is provided. Depending on the structure of the [[domain of a function|domain]] and [[codomain]] of ''g'', several techniques for approximating ''g'' may be applicable. For example, if ''g'' is an operation on the [[real number]]s, techniques of [[interpolation]], [[extrapolation]], [[regression analysis]], and [[curve fitting]] can be used. If the [[codomain]] (range or target set) of ''g'' is a finite set, one is dealing with a [[statistical classification|classification]] problem instead. A related problem of ''online'' time series approximation<ref>Gandhi, Sorabh, Luca Foschini, and Subhash Suri. "[https://ieeexplore.ieee.org/abstract/document/5447930/ Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order]." Data Engineering (ICDE), 2010 IEEE 26th International Conference on. IEEE, 2010.</ref> is to summarize the data in one-pass and construct an approximate representation that can support a variety of time series queries with bounds on worst-case error.<br /> <br /> Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points (a time series) of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. If the codomain (range or target set) of g is a finite set, one is dealing with a classification problem instead. A related problem of online time series approximationGandhi, Sorabh, Luca Foschini, and Subhash Suri. "Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order." Data Engineering (ICDE), 2010 IEEE 26th International Conference on. IEEE, 2010. is to summarize the data in one-pass and construct an approximate representation that can support a variety of time series queries with bounds on worst-case error.<br /> <br /> 其次，目标函数，称为 g，可能是未知的; 代替黎曼显式公式，只有一组形式(x，g (x))的点(时间序列)被提供。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。在线时间序列的一个相关问题接近于 andhi，Sorabh，Luca Foschini，和 Subhash Suri。时间序列数据的空间有效在线近似: 数据流、失忆和无序数据工程，2010年 IEEE 第26届国际会议。2010.是对数据进行一次总结，构造一个近似表示，可以支持各种时间序列查询，最坏情况下的错误界限。<br /> <br /> To some extent, the different problems ([[regression analysis|regression]], [[Statistical classification|classification]], [[fitness approximation]]) have received a unified treatment in [[statistical learning theory]], where they are viewed as [[supervised learning]] problems.<br /> <br /> To some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.<br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===Prediction and forecasting===<br /> In [[statistics]], [[prediction]] is a part of [[statistical inference]]. One particular approach to such inference is known as [[predictive inference]], but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as [[forecasting]].<br /> * Fully formed statistical models for [[stochastic simulation]] purposes, so as to generate alternative versions of the time series, representing what might happen over non-specific time-periods in the future<br /> * Simple or fully formed statistical models to describe the likely outcome of the time series in the immediate future, given knowledge of the most recent outcomes (forecasting).<br /> * Forecasting on time series is usually done using automated statistical software packages and programming languages, such as [[Julia (programming language)|Julia]], [[Python (programming language)|Python]], [[R (programming language)|R]], [[SAS (software)|SAS]], [[SPSS]] and many others.<br /> * Forecasting on large scale data can be done with [[Apache Spark]] using the Spark-TS library, a third-party package.<ref>{{cite web |title=Time Series Analysis with Spark |author=Sandy Ryza |date=2020-03-18 |access-date=2021-01-12 |url=https://databricks.com/session/time-series-analysis-with-spark |format=slides of a talk at Spark Summit East 2016 |publisher=[[Databricks]]}}</ref><br /> <br /> In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as forecasting.<br /> * Fully formed statistical models for stochastic simulation purposes, so as to generate alternative versions of the time series, representing what might happen over non-specific time-periods in the future<br /> * Simple or fully formed statistical models to describe the likely outcome of the time series in the immediate future, given knowledge of the most recent outcomes (forecasting).<br /> * Forecasting on time series is usually done using automated statistical software packages and programming languages, such as Julia, Python, R, SAS, SPSS and many others.<br /> * Forecasting on large scale data can be done with Apache Spark using the Spark-TS library, a third-party package.<br /> <br /> 在统计学中，预测是推论统计学的一部分。一种特殊的推理方法被称为预测推理，但是这种预测可以在几种推论统计学推理方法中的任何一种中进行。事实上，对统计的一种描述是，它提供了一种将关于某一人口样本的知识转移给整个人口和其他相关人口的手段，这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，这个过程就被称为预测。<br /> * 为随机模拟目的而建立完整的统计模型，以产生时间序列的替代版本，反映未来在非特定时间段内可能发生的情况 <br /> * 简单或完整的统计模型，以描述时间序列在最近期间可能产生的结果(预测)。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===Classification===<br /> {{main|Statistical classification}}<br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in [[sign language]].<br /> <br /> <br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in sign language.<br /> <br /> = = = 分类 = = 将时间序列模式分配到一个特定的类别，例如根据手语中的一系列动作识别一个单词。<br /> <br /> ===Signal estimation===<br /> {{see also|Signal processing|Estimation theory}}<br /> This approach is based on [[harmonic analysis]] and filtering of signals in the [[frequency domain]] using the [[Fourier transform]], and [[spectral density estimation]], the development of which was significantly accelerated during [[World War II]] by mathematician [[Norbert Wiener]], electrical engineers [[Rudolf E. Kálmán]], [[Dennis Gabor]] and others for filtering signals from noise and predicting signal values at a certain point in time. See [[Kalman filter]], [[Estimation theory]], and [[Digital signal processing]]<br /> <br /> <br /> This approach is based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation, the development of which was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. See Kalman filter, Estimation theory, and Digital signal processing<br /> <br /> = = = 信号估计 = = = 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，其发展是显着加速二战期间由数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯 Gabor 和其他人从噪音信号过滤和预测信号值在一定时间点。参见卡尔曼滤波器，参数估测和数字信号处理<br /> <br /> ===Segmentation===<br /> {{main|Time-series segmentation}}<br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using [[Change detection|change-point detection]], or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> <br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using change-point detection, or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> = = = 分割 = = 将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。在时间序列分割中，目标是识别时间序列中的分段边界点，并刻画每个分段的动态特性。人们可以通过变点检测来解决这个问题，或者将时间序列建模为一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ==Models==<br /> <br /> ==Models==<br /> <br /> = = 模型 = = <br /> <br /> Models for time series data can have many forms and represent different [[stochastic processes]]. When modeling variations in the level of a process, three broad classes of practical importance are the ''[[autoregressive]]'' (AR) models, the ''integrated'' (I) models, and the ''[[moving average model|moving average]]'' (MA) models. These three classes depend linearly on previous data points.<ref name="linear time series">{{cite book |author-link=Neil Gershenfeld |last=Gershenfeld |first=N. |year=1999 |title=The Nature of Mathematical Modeling |url=https://archive.org/details/naturemathematic00gers_334 |url-access=limited |location=New York |publisher=Cambridge University Press |pages=[https://archive.org/details/naturemathematic00gers_334/page/n206 205]–208 |isbn=978-0521570954 }}</ref> Combinations of these ideas produce [[autoregressive moving average]] (ARMA) and [[autoregressive integrated moving average]] (ARIMA) models. The [[autoregressive fractionally integrated moving average]] (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for [[vector autoregression]]. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> Models for time series data can have many forms and represent different stochastic processes. When modeling variations in the level of a process, three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. These three classes depend linearly on previous data points. Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models. The autoregressive fractionally integrated moving average (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector autoregression. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> 时间序列数据的模型可以有多种形式，表示不同的随机过程。在对过程层次的变化进行建模时，三大类实际的重要性是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个类线性地依赖于以前的数据点。这些想法的结合产生了自回归移动平均(ARMA)和 ARIMA模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对前三种模型进行了推广。处理矢量值数据的这些类的扩展可以在多元时间序列模型的标题下得到，有时前面的首字母缩略词被扩展，包括一个初始的“ v”代表“矢量”，如在 VAR 代表向量自回归模型。这些模型的另外一组扩展可用于观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应) : 与多变量情况的区别在于强迫序列可能是确定的或者在实验者的控制之下。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a [[chaos theory|chaotic]] time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in [[nonlinear autoregressive exogenous model]]s. Further references on nonlinear time series analysis: (Kantz and Schreiber),<ref>{{cite book|last1=Kantz|first1=Holger|last2=Thomas|first2=Schreiber|title=Nonlinear Time Series Analysis|date=2004|publisher=Cambridge University Press|location=London|isbn=978-0521529020}}</ref> and (Abarbanel)<ref>{{cite book|last1=Abarbanel|first1=Henry|title=Analysis of Observed Chaotic Data|date=Nov 25, 1997|publisher=Springer|location=New York|isbn=978-0387983721}}</ref><br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a chaotic time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in nonlinear autoregressive exogenous models. Further references on nonlinear time series analysis: (Kantz and Schreiber), and (Abarbanel)<br /> <br /> 一系列数据的水平对以前的数据点的非线性依赖是有趣的，部分是因为产生混沌时间序列的可能性。然而，更重要的是，经验调查可以表明使用来自非线性模型的预测优于来自线性模型的预测，例如在非线性自回归外生模型中。非线性时间序列分析的进一步参考文献: (Kantz 和 Schreiber)和(Abarbanel) <br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time ([[heteroskedasticity]]). These models represent [[autoregressive conditional heteroskedasticity]] (ARCH) and the collection comprises a wide variety of representation ([[GARCH]], TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a [[doubly stochastic model]].<br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time (heteroskedasticity). These models represent autoregressive conditional heteroskedasticity (ARCH) and the collection comprises a wide variety of representation (GARCH, TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a doubly stochastic model.<br /> <br /> 在其他类型的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型代表了 ARCH模型(ARCH) ，收藏包括各种各样的代表(GARCH，TARCH，EGARCH，FIGARCH，CGARCH 等等)。在这里，变异性的变化与观测系列的最近过去的值有关，或者是预测的。这与局部变化的其他可能表现形式形成对比，在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also [[Markov switching multifractal]] (MSMF) techniques for modeling volatility evolution.<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution.<br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列，试图说明在多个尺度上的时间依赖。参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> A [[Hidden Markov model]] (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest [[dynamic Bayesian network]]. HMM models are widely used in [[speech recognition]], for translating a time series of spoken words into text.<br /> <br /> A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.<br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔科姆可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，用于将语音序列转换成文本。<br /> <br /> ===Notation===<br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series ''X'' that is indexed by the [[natural number]]s is written<br /> :''X'' = (''X''<sub>1</sub>, ''X''<sub>2</sub>, ...).<br /> <br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written<br /> :X = (X1, X2, ...).<br /> <br /> = = = 表示法 = = 用于时间序列分析的许多不同的表示法。一个用于指定时间序列 x 的通用符号是: x = (X1，X2，...)。<br /> <br /> Another common notation is<br /> :''Y'' = (''Y<sub>t</sub>'': ''t'' ∈ ''T''),<br /> where ''T'' is the [[index set]].<br /> <br /> Another common notation is<br /> :Y = (Yt: t ∈ T),<br /> where T is the index set.<br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===Conditions===<br /> There are two sets of conditions under which much of the theory is built:<br /> * [[Stationary process]]<br /> * [[Ergodic process]]<br /> <br /> There are two sets of conditions under which much of the theory is built:<br /> * Stationary process<br /> * Ergodic process<br /> <br /> 这个理论的大部分建立在两个条件之下: <br /> * 平稳过程遍历过程<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: [[strict stationarity]] and [[Stationary process#Weaker forms of stationarity|second-order stationarity]]. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: strict stationarity and second-order stationarity. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> 然而，平稳性的概念必须扩展到考虑两个重要的概念: 严格平稳性和二阶平稳性。模型和应用程序都可以在这些条件中的每一种情况下开发，尽管后一种情况下的模型可能被认为只是部分具体说明。<br /> <br /> In addition, time-series analysis can be applied where the series are [[Cyclostationary process|seasonally stationary]] or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in [[time-frequency analysis]] which makes use of a [[time–frequency representation]] of a time-series or signal.<ref>Boashash, B. (ed.), (2003) ''Time-Frequency Signal Analysis and Processing: A Comprehensive Reference'', Elsevier Science, Oxford, 2003 {{isbn|0-08-044335-4}}</ref><br /> <br /> In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.Boashash, B. (ed.), (2003) Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003 <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或非平稳的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。波阿什，b。我不知道你在说什么。) ，(2003)《时频信号分析与处理: 综合参考》，爱思唯尔科学出版社，牛津，2003<br /> <br /> ===Tools===<br /> Tools for investigating time-series data include:<br /> <br /> Tools for investigating time-series data include:<br /> <br /> = = = 调查时间序列数据的工具包括:<br /> <br /> * Consideration of the [[autocorrelation|autocorrelation function]] and the [[Spectral density|spectral density function]] (also [[cross-correlation function]]s and cross-spectral density functions)<br /> * [[Scaled correlation|Scaled]] cross- and auto-correlation functions to remove contributions of slow components<ref name="Nikolicetal">{{cite journal |last1=Nikolić |first1=D. |last2=Muresan |first2=R. C. |last3=Feng |first3=W. |last4=Singer |first4=W. |year=2012 |title=Scaled correlation analysis: a better way to compute a cross-correlogram |journal=European Journal of Neuroscience |volume=35 |issue=5 |pages=742–762 |doi=10.1111/j.1460-9568.2011.07987.x |pmid=22324876 |s2cid=4694570 |url=https://semanticscholar.org/paper/caa784fc3c22656413143559c402b54d0567f4d1 }}</ref><br /> * Performing a [[Fourier transform]] to investigate the series in the [[frequency domain]]<br /> * Use of a [[digital filter|filter]] to remove unwanted [[noise (physics)|noise]]<br /> * [[Principal component analysis]] (or [[empirical orthogonal function]] analysis)<br /> * [[Singular spectrum analysis]]<br /> * "Structural" models:<br /> ** General [[State Space Model]]s<br /> ** Unobserved Components Models<br /> * [[Machine Learning]]<br /> ** [[Artificial neural network]]s<br /> ** [[Support vector machine]]<br /> ** [[Fuzzy logic]]<br /> ** [[Gaussian process]]<br /> ** [[Genetic Programming]]<br /> ** [[Gene expression programming]]<br /> ** [[Hidden Markov model]]<br /> ** [[Multi expression programming]]<br /> * [[Queueing theory]] analysis<br /> * [[Control chart]]<br /> ** [[Shewhart individuals control chart]]<br /> ** [[CUSUM]] chart<br /> ** [[EWMA chart]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Nonlinear mixed-effects model|Nonlinear mixed-effects modeling]]<br /> * [[Dynamic time warping]]<ref name="Sakoe 1978">{{cite book |last1=Sakoe |first1=Hiroaki |last2=Chiba |first2=Seibi |year=1978 |chapter=Dynamic programming algorithm optimization for spoken word recognition |volume=26 |pages=43–49 |doi=10.1109/TASSP.1978.1163055 |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |s2cid=17900407 |chapter-url=https://semanticscholar.org/paper/18f355d7ef4aa9f82bf5c00f84e46714efa5fd77 }}</ref><br /> * [[Cross-correlation]]<ref>{{cite book |last1=Goutte |first1=Cyril |last2=Toft |first2=Peter |last3=Rostrup |first3=Egill |last4=Nielsen |first4=Finn Å. |last5=Hansen |first5=Lars Kai |year=1999 |chapter=On Clustering fMRI Time Series |volume=9 |issue=3 |pages=298–310 |doi=10.1006/nimg.1998.0391 |pmid=10075900 |journal=NeuroImage |s2cid=14147564 |chapter-url=https://semanticscholar.org/paper/2d5c663fb53d8348bdf3c4df0f881b5db2dcf5e3 }}</ref><br /> * [[Dynamic Bayesian network]]<br /> * [[Time-frequency representation|Time-frequency analysis techniques:]]<br /> ** [[Fast Fourier transform]]<br /> ** [[Continuous wavelet transform]]<br /> ** [[Short-time Fourier transform]]<br /> ** [[Chirplet transform]]<br /> ** [[Fractional Fourier transform]]<br /> * [[Chaos theory|Chaotic analysis]]<br /> ** [[Correlation dimension]]<br /> ** [[Recurrence plot]]s<br /> ** [[Recurrence quantification analysis]]<br /> ** [[Lyapunov exponent]]s<br /> ** [[Entropy encoding]]<br /> <br /> * Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions)<br /> * Scaled cross- and auto-correlation functions to remove contributions of slow components<br /> * Performing a Fourier transform to investigate the series in the frequency domain<br /> * Use of a filter to remove unwanted noise<br /> * Principal component analysis (or empirical orthogonal function analysis)<br /> * Singular spectrum analysis<br /> * "Structural" models:<br /> ** General State Space Models<br /> ** Unobserved Components Models<br /> * Machine Learning<br /> ** Artificial neural networks<br /> ** Support vector machine<br /> ** Fuzzy logic<br /> ** Gaussian process<br /> ** Genetic Programming<br /> ** Gene expression programming<br /> ** Hidden Markov model<br /> ** Multi expression programming<br /> * Queueing theory analysis<br /> * Control chart<br /> ** Shewhart individuals control chart<br /> ** CUSUM chart<br /> ** EWMA chart<br /> * Detrended fluctuation analysis<br /> * Nonlinear mixed-effects modeling<br /> * Dynamic time warping<br /> * Cross-correlation<br /> * Dynamic Bayesian network<br /> * Time-frequency analysis techniques:<br /> ** Fast Fourier transform<br /> ** Continuous wavelet transform<br /> ** Short-time Fourier transform<br /> ** Chirplet transform<br /> ** Fractional Fourier transform<br /> * Chaotic analysis<br /> ** Correlation dimension<br /> ** Recurrence plots<br /> ** Recurrence quantification analysis<br /> ** Lyapunov exponents<br /> ** Entropy encoding<br /> <br /> <br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数) <br /> * 调整互相关函数和自相关函数以去除慢分量的贡献 <br /> * 在频域中执行一个傅里叶变换来调查这个序列 <br /> * 使用<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图 <br /> * <br /> * EWMA 图 <br /> * 非趋势波动分析 <br /> * 非线性混合效应建模 <br /> * <br /> * 动态时间规整互相关 <br /> * <br /> * 动态贝氏网路 <br /> * 时频分析技术: <br /> * <br /> * 快速傅里叶变换连续小波转换 <br /> * <br /> * 短时距傅里叶变换 <br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析 <br /> * <br /> * <br /> * 复发图 <br /> * <br /> * 递归量化分析 <br /> * <br /> * Lyapunov 指数 <br /> * <br /> * <br /> * <br /> * <br /> <br /> ===Measures===<br /> Time series metrics or [[Features (pattern recognition)|features]] that can be used for time series [[Classification (machine learning)|classification]] or [[regression analysis]]:<ref>{{cite journal |last1=Mormann |first1=Florian |last2=Andrzejak |first2=Ralph G. |last3=Elger |first3=Christian E. |last4=Lehnertz |first4=Klaus |title=Seizure prediction: the long and winding road |journal=[[Brain (journal)|Brain]] |year=2007 |volume=130 |issue=2 |pages=314–333 |doi=10.1093/brain/awl241 |pmid=17008335|doi-access=free }}</ref><br /> <br /> Time series metrics or features that can be used for time series classification or regression analysis:<br /> <br /> = = = = 可用于时间序列分类或回归分析的时间序列度量或特征:<br /> <br /> * '''Univariate linear measures'''<br /> ** [[Moment (mathematics)]]<br /> ** [[Spectral band power]]<br /> ** [[Spectral edge frequency]]<br /> ** Accumulated [[Energy (signal processing)]]<br /> ** Characteristics of the [[autocorrelation]] function<br /> ** [[Hjorth parameters]]<br /> ** [[Fast Fourier transform|FFT]] parameters<br /> ** [[Autoregressive model]] parameters<br /> ** [[Mann–Kendall test]]<br /> * '''Univariate non-linear measures'''<br /> ** Measures based on the [[correlation]] sum<br /> ** [[Correlation dimension]]<br /> ** [[Correlation integral]]<br /> ** [[Correlation density]]<br /> ** [[Correlation entropy]]<br /> ** [[Approximate entropy]]<ref>{{cite web |last1=Land |first1=Bruce |last2=Elias |first2=Damian |title=Measuring the 'Complexity' of a time series |url=http://www.nbb.cornell.edu/neurobio/land/PROJECTS/Complexity/ }}</ref><br /> ** [[Sample entropy]]<br /> ** {{iw2|Fourier entropy||uk|Ентропія Фур'є}}<br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** [[Rényi entropy]]<br /> ** Higher-order methods<br /> ** [[Marginal predictability]]<br /> ** [[Dynamical similarity]] index<br /> ** [[State space]] dissimilarity measures<br /> ** [[Lyapunov exponent]]<br /> ** Permutation methods<br /> ** [[Local flow]]<br /> * '''Other univariate measures'''<br /> ** [[Algorithmic information theory|Algorithmic complexity]]<br /> ** [[Kolmogorov complexity]] estimates<br /> ** [[Hidden Markov Model]] states<br /> ** [[Rough path#Signature|Rough path signature]]<ref>[1] Chevyrev, I., Kormilitzin, A. (2016) "[https://arxiv.org/abs/1603.03788 A Primer on the Signature Method in Machine Learning], arXiv:1603.03788v1"</ref><br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * '''Bivariate linear measures'''<br /> ** Maximum linear [[cross-correlation]]<br /> ** Linear [[Coherence (signal processing)]]<br /> * '''Bivariate non-linear measures'''<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for [[Phase synchronization]]<br /> ** Measures for [[Phase locking]]<br /> * '''Similarity measures''':<ref>{{cite journal |last1=Ropella |first1=G. E. P. |last2=Nag |first2=D. A. |last3=Hunt |first3=C. A. |title=Similarity measures for automated comparison of in silico and in vitro experimental results |journal=Engineering in Medicine and Biology Society |year=2003 |volume=3 |pages=2933–2936 |doi=10.1109/IEMBS.2003.1280532 |isbn=978-0-7803-7789-9 |s2cid=17798157 }}</ref><br /> ** [[Cross-correlation]]<br /> ** [[Dynamic Time Warping]]<ref name="Sakoe 1978"/><br /> ** [[Hidden Markov Models]]<br /> ** [[Edit distance]]<br /> ** [[Total correlation]]<br /> ** [[Newey–West estimator]]<br /> ** [[Prais–Winsten estimation|Prais–Winsten transformation]]<br /> ** Data as Vectors in a Metrizable Space<br /> *** [[Minkowski distance]]<br /> *** [[Mahalanobis distance]]<br /> ** Data as time series with envelopes<br /> *** Global [[standard deviation]]<br /> *** Local [[standard deviation]]<br /> *** Windowed [[standard deviation]]<br /> ** Data interpreted as stochastic series<br /> *** [[Pearson product-moment correlation coefficient]]<br /> *** [[Spearman's rank correlation coefficient]]<br /> ** Data interpreted as a [[probability distribution]] function<br /> *** [[Kolmogorov–Smirnov test]]<br /> *** [[Cramér–von Mises criterion]]<br /> <br /> * Univariate linear measures<br /> ** Moment (mathematics)<br /> ** Spectral band power<br /> ** Spectral edge frequency<br /> ** Accumulated Energy (signal processing)<br /> ** Characteristics of the autocorrelation function<br /> ** Hjorth parameters<br /> ** FFT parameters<br /> ** Autoregressive model parameters<br /> ** Mann–Kendall test<br /> * Univariate non-linear measures<br /> ** Measures based on the correlation sum<br /> ** Correlation dimension<br /> ** Correlation integral<br /> ** Correlation density<br /> ** Correlation entropy<br /> ** Approximate entropy<br /> ** Sample entropy<br /> ** <br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** Rényi entropy<br /> ** Higher-order methods<br /> ** Marginal predictability<br /> ** Dynamical similarity index<br /> ** State space dissimilarity measures<br /> ** Lyapunov exponent<br /> ** Permutation methods<br /> ** Local flow<br /> * Other univariate measures<br /> ** Algorithmic complexity<br /> ** Kolmogorov complexity estimates<br /> ** Hidden Markov Model states<br /> ** Rough path signature[1] Chevyrev, I., Kormilitzin, A. (2016) "A Primer on the Signature Method in Machine Learning, arXiv:1603.03788v1"<br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * Bivariate linear measures<br /> ** Maximum linear cross-correlation<br /> ** Linear Coherence (signal processing)<br /> * Bivariate non-linear measures<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for Phase synchronization<br /> ** Measures for Phase locking<br /> * Similarity measures:<br /> ** Cross-correlation<br /> ** Dynamic Time Warping<br /> ** Hidden Markov Models<br /> ** Edit distance<br /> ** Total correlation<br /> ** Newey–West estimator<br /> ** Prais–Winsten transformation<br /> ** Data as Vectors in a Metrizable Space<br /> *** Minkowski distance<br /> *** Mahalanobis distance<br /> ** Data as time series with envelopes<br /> *** Global standard deviation<br /> *** Local standard deviation<br /> *** Windowed standard deviation<br /> ** Data interpreted as stochastic series<br /> *** Pearson product-moment correlation coefficient<br /> *** Spearman's rank correlation coefficient<br /> ** Data interpreted as a probability distribution function<br /> *** Kolmogorov–Smirnov test<br /> *** Cramér–von Mises criterion<br /> <br /> <br /> * 单变量线性测量 <br /> * <br /> * 矩(数学) <br /> * <br /> * 谱带功率 <br /> * <br /> * 谱边缘频率 <br /> * <br /> * 累积能量(信号处理) <br /> * <br /> * 自相关函数特性 <br /> * <br /> * Hjorth 参数 <br /> * <br /> * FFT 参数 <br /> * <br /> * 自回归模型参数 <br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流 <br /> * 其他单变量度量 <br /> * <br /> * 算法复杂度 <br /> * <br /> * 柯氏复杂性估计 <br /> * <br /> * 隐马尔可夫模型状态 <br /> * <br /> * 粗糙路径签名[1] Chevyrev，i. ，Kormilitzin，a。(2016)“ a Primer on the Signature Method in Machine Learning，arXiv: 1603.03788 v1”<br /> * <br /> * 替代时间序列和替代校正 <br /> * <br /> * 递归损失(非平稳度) <br /> * 双变量线性度量 <br /> * <br /> * 最大线性互相关 <br /> * <br /> * 线性相干性(信号处理) <br /> * 双变量非线性度量 <br /> * <br /> * 非线性相互依赖 <br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学) <br /> * <br /> * 相位同步的度量 <br /> * <br /> * 相位锁定的度量 <br /> * <br /> * 相似度量: <br /> * <br /> * 互相关 <br /> * <br /> * <br /> * 动态时间规整 <br /> * <br /> * <br /> * 隐马尔可夫模型 <br /> * <br /> * <br /> * 编辑距离 <br /> * <br /> * 总相关性 <br /> * <br /> * Newey-West 估计 <br /> * <br /> * Prais-Winsten 变换 <br /> * <br /> * 数据作为向量在乌雷松度量化定理 <br /> * <br /> * <br /> * 明氏距离 <br /> * <br /> * 马氏距离 <br /> * <br /> * 数据作为时间序列与信封 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差标准差 <br /> * <br /> * <br /> * 窗口标准差 <br /> * <br /> * 数据解释为随机序列 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数 <br /> * <br /> * 数据解释为概率分布函数 <br /> * <br /> * Kolmogorov-Smirnov 检验 <br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ==Visualization==<br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<ref>{{cite web|last1=Tominski|first1=Christian|last2= Aigner|first2=Wolfgang|title=The TimeViz Browser:A Visual Survey of Visualization Techniques for Time-Oriented Data|url=http://survey.timeviz.net/|access-date=1 June 2014}}</ref><br /> <br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<br /> <br /> = = 可视化 = = 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> ===Overlapping charts===<br /> * [[Braided graphs]]<br /> * Line charts<br /> * Slope graphs<br /> * {{iw2|GapChart||fr}}<br /> <br /> * Braided graphs<br /> * Line charts<br /> * Slope graphs<br /> * <br /> <br /> = = = = 重叠图 = = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> ===Separated charts===<br /> * [[Horizon graphs]]<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> * Horizon graphs<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> = = = = = 分离图表 = = = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ==See also==<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ==References==<br /> {{Reflist|2}}<br /> <br /> ==Further reading==<br /> * {{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> * [[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> * {{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> * {{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> * [[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]]. {{ISBN|978-0-12-564901-8}}<br /> * {{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer, {{ISBN|978-3-319-52451-1}}<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> * [[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> * {{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> = = 进一步阅读 = = <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社。<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社。<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去。北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社。<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社。<br /> *<br /> <br /> ==External links==<br /> {{Commons category}}<br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> <br /> *Introduction to Time series Analysis (Engineering Statistics Handbook) — A practical guide to Time series analysis.<br /> <br /> = = 外部链接 = = <br /> * 时间序列分析导论(工程统计手册)ー时间序列分析实用指南。<br /> <br /> {{Statistics}}<br /> {{Portal bar|Mathematics}}<br /> {{Authority control}}<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> <br /> <br /> <br /> Category:Statistical data types<br /> Category:Mathematical and quantitative methods (economics)<br /> Category:Machine learning<br /> <br /> 类别: 统计数据类型类别: 数学和定量方法(经济学)类别: 机器学习<br /> <br /> <noinclude><br /> <br /> <small>This page was moved from [[wikipedia:en:Time series]]. Its edit history can be viewed at [[时间序列分析/edithistory]]</small></noinclude><br /> <br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33945 时间序列分析 2023-02-05T03:35:08Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> <br /> <br /> 时间序列分析是对按时间顺序导出的(或列出或绘制)的一系列数据点进行分析。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> 时间序列分析需要提取时间序列数据中有意义的统计特征以及数据的其他特征。时间序列分析涉及到时间序列的预测。时间序列预测是一种基于先前观测到的值去使用模型来预测未来值的方法。虽然回归分析经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系，也会分析被干预的时间序列（分析时间序列在接受干预前后的变化）。这种干预可能会影响基础变量。<br /> <br /> <br /> <br /> <br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究。在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性）。<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数值Numeric数据或离散符号数据（即字符序列，如英语中的字母和单词<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>）。<br /> ==分析方法==<br /> <br /> <br /> 时间序列分析的方法可分为两类：频域方法和时域方法。前者包括频谱分析和小波分析；后者包括自相关和交叉相关分析。在时域中，可以用类似于滤波器的方式使用标度相关性来进行关联和分析。<br /> <br /> 此外，时间序列分析技术可分为参数化和非参数化方法。参数方法假定基础的平稳随机过程具有某种结构，可以用少量的参数来描述（例如，使用自回归或移动平均模型）。在这些方法中，时间序列分析的任务是估计描述随机过程的模型的参数。相比之下，非参数方法明确地估计过程的协方差或频谱，而不假设过程有任何特定的结构。<br /> <br /> <br /> <br /> <br /> <br /> 时间序列分析的方法也可以分为线性和非线性，以及单变量和多变量。<br /> <br /> ==面板数据==<br /> A time series is one type of [[panel data]]. Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a [[cross-sectional data]]set). A data set may exhibit characteristics of both panel data and time series data. One way to tell is to ask what makes one data record unique from the other records. If the answer is the time data field, then this is a time series data set candidate. If determining a unique record requires a time data field and an additional identifier which is unrelated to time (e.g. student ID, stock symbol, country code), then it is panel data candidate. If the differentiation lies on the non-time identifier, then the data set is a cross-sectional data set candidate.<br /> <br /> 时间序列是面板数据的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断的方法之一是探究是什么使一条数据记录与其他记录不同。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==Analysis分析==<br /> There are several types of motivation and data analysis available for time series which are appropriate for different purposes.<br /> <br /> 对于具有不同目的的时间序列，适用的动机和数据分析方法都不同。<br /> <br /> ===Motivation动机===<br /> In the context of [[statistics]], [[econometrics]], [[quantitative finance]], [[seismology]], [[meteorology]], and [[geophysics]] the primary goal of time series analysis is [[forecasting]]. In the context of [[signal processing]], [[control engineering]] and [[communication engineering]] it is used for signal detection. Other applications are in [[data mining]], [[pattern recognition]] and [[machine learning]], where time series analysis can be used for [[cluster analysis|clustering]],<ref name=":1">{{cite journal | last1 = Liao | first1 = T. Warren | title = Clustering of time series data - a survey | journal = Pattern Recognition | volume = 38 | issue = 11 | pages = 1857–1874 | publisher = Elsevier | date = 2005 | language = en | doi = 10.1016/j.patcog.2005.01.025| bibcode = 2005PatRe..38.1857W }}{{subscription required|via=ScienceDirect }}</ref><ref name=":2">{{cite journal | last1 = Aghabozorgi | first1 = Saeed | last2 = Shirkhorshidi | first2 = Ali S. | last3 = Wah | first3 = Teh Y. | title = Time-series clustering – A decade review | journal = Information Systems | volume = 53 | pages = 16–38 | publisher = Elsevier | date = 2015 | language = en | doi = 10.1016/j.is.2015.04.007}}{{subscription required|via=ScienceDirect }}</ref> [[Statistical classification|classification]],<ref name=":3">{{cite journal | last1 = Keogh | first1 = Eamonn J. | title = On the need for time series data mining benchmarks | journal = Data Mining and Knowledge Discovery | volume = 7 | pages = 349–371 | publisher = Kluwer | date = 2003 | language = en | doi = 10.1145/775047.775062| isbn = 158113567X | s2cid = 41617550 }}{{subscription required|via=ACM Digital Library }}</ref> query by content,<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref> [[anomaly detection]] as well as [[forecasting]].<ref name=":5">{{cite journal|last1=Chen|first1=Cathy W. S.|last2=Chiu|first2=L. M.|date=September 2021|title=Ordinal Time Series Forecasting of the Air Quality Index|journal=Entropy|language=en|volume=23|issue=9|pages=1167|doi=10.3390/e23091167|pmid=34573792|pmc=8469594|bibcode=2021Entrp..23.1167C|doi-access=free}}</ref><br /> <br /> 在统计学Statistics、计量经济学Econometrics、定量金融学Quantitative finance、地震学Seismology、气象学Meteorology和地球物理学Geophysics方面，时间序列分析的主要目标是预测Forecasting。在信号处理Signal processing、控制工程Control engineering和通信工程Communication engineering方面，它被用于信号检测。在数据挖掘Data mining、模式识别Pattern recognition和机器学习Machine learning等其他应用中，时间序列分析可用于聚类Clustering<ref name=":1" /><ref name=":2" />、分类Classification<ref name=":3" />、按内容查询<ref name=":4" />、异常检测Anomaly detection以及预测Forecasting<ref name=":5" />。<br /> <br /> ===Exploratory analysis探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> {{further|Exploratory analysis}}<br /> A straightforward way to examine a regular time series is manually with a [[line chart]]. An example chart is shown on the right for tuberculosis incidence in the United States, made with a spreadsheet program. The number of cases was standardized to a rate per 100,000 and the percent change per year in this rate was calculated. The nearly steadily dropping line shows that the TB incidence was decreasing in most years, but the percent change in this rate varied by as much as +/- 10%, with 'surges' in 1975 and around the early 1990s. The use of both vertical axes allows the comparison of two time series in one graphic.<br /> <br /> 绘制折线图Line chart是检查常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，使得可以在一个图表中比较两个时间序列。<br /> <br /> <br /> A study of corporate data analysts found two challenges to exploratory time series analysis: discovering the shape of interesting patterns, and finding an explanation for these patterns.<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref> Visual tools that represent time series data as [[Heat map|heat map matrices]] can help overcome these challenges.<br /> <br /> 一项对企业数据分析师的研究发现，探索性时间序列分析有两个挑战：发现有趣模式，以及为这些模式找到解释<ref name=":6" />。将时间序列数据可视化为热力图矩阵Heat map matrices的工具可以帮助克服这些挑战。<br /> <br /> <br /> Other techniques include:<br /> <br /> 其他技巧包括:<br /> <br /> * [[Autocorrelation]] analysis to examine [[serial dependence]]<br /> * [[frequency spectrum#Spectrum analysis|Spectral analysis]] to examine cyclic behavior which need not be related to [[seasonality]]. For example, sunspot activity varies over 11 year cycles.<ref>{{cite book |last=Bloomfield |first=P. |year=1976 |title=Fourier analysis of time series: An introduction |location=New York |publisher=Wiley |isbn=978-0471082569 }}</ref><ref>{{cite book |last=Shumway |first=R. H. |year=1988 |title=Applied statistical time series analysis |location=Englewood Cliffs, NJ |publisher=Prentice Hall |isbn=978-0130415004 }}</ref> Other common examples include celestial phenomena, weather patterns, neural activity, commodity prices, and economic activity.<br /> * Separation into components representing trend, seasonality, slow and fast variation, and cyclical irregularity: see [[trend estimation]] and [[decomposition of time series]]<br /> <br /> * 自相关分析检验序列相关性；<br /> * 频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。其他常见的例子包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分：见趋势估计和时间序列的分。<br /> <br /> ===Curve fitting曲线拟合===<br /> {{main|Curve fitting}}<br /> <br /> Curve fitting<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> is the process of constructing a [[curve]], or [[function (mathematics)|mathematical function]], that has the best fit to a series of [[data]] points,<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref> possibly subject to constraints.<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref> Curve fitting can involve either [[interpolation]],<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref> where an exact fit to the data is required, or [[smoothing]],<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref> in which a "smooth" function is constructed that approximately fits the data. A related topic is [[regression analysis]],<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref> which focuses more on questions of [[statistical inference]] such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization,<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref> to infer values of a function where no data are available,<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref> and to summarize the relationships among two or more variables.<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref> [[Extrapolation]] refers to the use of a fitted curve beyond the [[range (statistics)|range]] of the observed data,<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref> and is subject to a [[Uncertainty|degree of uncertainty]]<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref> since it may reflect the method used to construct the curve as much as it reflects the observed data.<br /> <br /> 正文：曲线拟合Curve fitting<br /> <br /> 曲线拟合<ref name=":7" /><ref name=":8" /> 是构建一条曲线Curve或数学函数Mathematical function的过程，它对一系列的数据Data点具有最佳的拟合效果<ref name=":9" />，可能会受到一些限制<ref name=":10" /><ref name=":11" />。曲线拟合包括插值Interpolation<ref name=":12" /><ref name=":13" />（需要精确地拟合数据）与平滑Smoothing<ref name=":14" /><ref name=":15" />（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析Regression analysis<ref name=":16" /><ref name=":17" />更侧重于统计推断Statistical inference的问题。例如，在拟合有随机误差的数据的曲线中，有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18" /><ref name=":19" />，在没有数据的情况下推断函数的值<ref name=":20" />，并总结两个或多个变量之间的关系<ref name=":21" />。外推法Extrapolation是指在观测到的数据范围Range之外使用拟合曲线<ref name=":22" />，它有一定程度的不确定性Degree of uncertainty<ref name=":23" />，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> <br /> The construction of economic time series involves the estimation of some components for some dates by [[interpolation]] between values ("benchmarks") for earlier and later dates. Interpolation is estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from the available information ("reading between the lines").<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref> Interpolation is useful where the data surrounding the missing data is available and its trend, seasonality, and longer-term cycles are known. This is often done by using a related series known for all relevant dates.<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref> Alternatively [[polynomial interpolation]] or [[spline interpolation]] is used where piecewise [[polynomial]] functions are fit into time intervals such that they fit smoothly together. A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function (also called [[Polynomial regression|regression]]).The main difference between regression and interpolation is that polynomial regression gives a single polynomial that models the entire data set. Spline interpolation, however, yield a piecewise continuous function composed of many polynomials to model the data set.<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的值（“基准”）之间进行插值Interpolation来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24" />。如果围绕缺失数据的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25" />。或者使用多项式插值Polynomial interpolation或样条插值Spline interpolation，将分段多项式Polynomial函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归Regression）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而样条插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> [[Extrapolation]] is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable. It is similar to [[interpolation]], which produces estimates between known observations, but extrapolation is subject to greater [[uncertainty]] and a higher risk of producing meaningless results.<br /> <br /> 外推法Extrapolation是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值Interpolation类似，插值在已知的观测值之间产生估计值，但外推法的不确定性Uncertainty更大，产生无意义结果的风险也更大。<br /> <br /> ===Function approximation===<br /> {{main|Function approximation}}<br /> In general, a function approximation problem asks us to select a [[function (mathematics)|function]] among a well-defined class that closely matches ("approximates") a target function in a task-specific way.<br /> One can distinguish two major classes of function approximation problems: First, for known target functions, [[approximation theory]] is the branch of [[numerical analysis]] that investigates how certain known functions (for example, [[special function]]s) can be approximated by a specific class of functions (for example, [[polynomial]]s or [[rational function]]s) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).<br /> <br /> <br /> In general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way.<br /> One can distinguish two major classes of function approximation problems: First, for known target functions, approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions) can be approximated by a specific class of functions (for example, polynomials or rational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).<br /> <br /> = = = = = = = = 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配(“近似”)。人们可以区分两类主要的函数逼近问题: 首先，对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数(例如，特殊函数)如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(廉价计算、连续性、积分和极限值等等)。).<br /> <br /> Second, the target function, call it ''g'', may be unknown; instead of an explicit formula, only a set of points (a time series) of the form (''x'', ''g''(''x'')) is provided. Depending on the structure of the [[domain of a function|domain]] and [[codomain]] of ''g'', several techniques for approximating ''g'' may be applicable. For example, if ''g'' is an operation on the [[real number]]s, techniques of [[interpolation]], [[extrapolation]], [[regression analysis]], and [[curve fitting]] can be used. If the [[codomain]] (range or target set) of ''g'' is a finite set, one is dealing with a [[statistical classification|classification]] problem instead. A related problem of ''online'' time series approximation<ref>Gandhi, Sorabh, Luca Foschini, and Subhash Suri. "[https://ieeexplore.ieee.org/abstract/document/5447930/ Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order]." Data Engineering (ICDE), 2010 IEEE 26th International Conference on. IEEE, 2010.</ref> is to summarize the data in one-pass and construct an approximate representation that can support a variety of time series queries with bounds on worst-case error.<br /> <br /> Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points (a time series) of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. If the codomain (range or target set) of g is a finite set, one is dealing with a classification problem instead. A related problem of online time series approximationGandhi, Sorabh, Luca Foschini, and Subhash Suri. "Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order." Data Engineering (ICDE), 2010 IEEE 26th International Conference on. IEEE, 2010. is to summarize the data in one-pass and construct an approximate representation that can support a variety of time series queries with bounds on worst-case error.<br /> <br /> 其次，目标函数，称为 g，可能是未知的; 代替黎曼显式公式，只有一组形式(x，g (x))的点(时间序列)被提供。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。在线时间序列的一个相关问题接近于 andhi，Sorabh，Luca Foschini，和 Subhash Suri。时间序列数据的空间有效在线近似: 数据流、失忆和无序数据工程，2010年 IEEE 第26届国际会议。2010.是对数据进行一次总结，构造一个近似表示，可以支持各种时间序列查询，最坏情况下的错误界限。<br /> <br /> To some extent, the different problems ([[regression analysis|regression]], [[Statistical classification|classification]], [[fitness approximation]]) have received a unified treatment in [[statistical learning theory]], where they are viewed as [[supervised learning]] problems.<br /> <br /> To some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.<br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===Prediction and forecasting===<br /> In [[statistics]], [[prediction]] is a part of [[statistical inference]]. One particular approach to such inference is known as [[predictive inference]], but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as [[forecasting]].<br /> * Fully formed statistical models for [[stochastic simulation]] purposes, so as to generate alternative versions of the time series, representing what might happen over non-specific time-periods in the future<br /> * Simple or fully formed statistical models to describe the likely outcome of the time series in the immediate future, given knowledge of the most recent outcomes (forecasting).<br /> * Forecasting on time series is usually done using automated statistical software packages and programming languages, such as [[Julia (programming language)|Julia]], [[Python (programming language)|Python]], [[R (programming language)|R]], [[SAS (software)|SAS]], [[SPSS]] and many others.<br /> * Forecasting on large scale data can be done with [[Apache Spark]] using the Spark-TS library, a third-party package.<ref>{{cite web |title=Time Series Analysis with Spark |author=Sandy Ryza |date=2020-03-18 |access-date=2021-01-12 |url=https://databricks.com/session/time-series-analysis-with-spark |format=slides of a talk at Spark Summit East 2016 |publisher=[[Databricks]]}}</ref><br /> <br /> In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as forecasting.<br /> * Fully formed statistical models for stochastic simulation purposes, so as to generate alternative versions of the time series, representing what might happen over non-specific time-periods in the future<br /> * Simple or fully formed statistical models to describe the likely outcome of the time series in the immediate future, given knowledge of the most recent outcomes (forecasting).<br /> * Forecasting on time series is usually done using automated statistical software packages and programming languages, such as Julia, Python, R, SAS, SPSS and many others.<br /> * Forecasting on large scale data can be done with Apache Spark using the Spark-TS library, a third-party package.<br /> <br /> 在统计学中，预测是推论统计学的一部分。一种特殊的推理方法被称为预测推理，但是这种预测可以在几种推论统计学推理方法中的任何一种中进行。事实上，对统计的一种描述是，它提供了一种将关于某一人口样本的知识转移给整个人口和其他相关人口的手段，这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，这个过程就被称为预测。<br /> * 为随机模拟目的而建立完整的统计模型，以产生时间序列的替代版本，反映未来在非特定时间段内可能发生的情况 <br /> * 简单或完整的统计模型，以描述时间序列在最近期间可能产生的结果(预测)。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===Classification===<br /> {{main|Statistical classification}}<br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in [[sign language]].<br /> <br /> <br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in sign language.<br /> <br /> = = = 分类 = = 将时间序列模式分配到一个特定的类别，例如根据手语中的一系列动作识别一个单词。<br /> <br /> ===Signal estimation===<br /> {{see also|Signal processing|Estimation theory}}<br /> This approach is based on [[harmonic analysis]] and filtering of signals in the [[frequency domain]] using the [[Fourier transform]], and [[spectral density estimation]], the development of which was significantly accelerated during [[World War II]] by mathematician [[Norbert Wiener]], electrical engineers [[Rudolf E. Kálmán]], [[Dennis Gabor]] and others for filtering signals from noise and predicting signal values at a certain point in time. See [[Kalman filter]], [[Estimation theory]], and [[Digital signal processing]]<br /> <br /> <br /> This approach is based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation, the development of which was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. See Kalman filter, Estimation theory, and Digital signal processing<br /> <br /> = = = 信号估计 = = = 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，其发展是显着加速二战期间由数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯 Gabor 和其他人从噪音信号过滤和预测信号值在一定时间点。参见卡尔曼滤波器，参数估测和数字信号处理<br /> <br /> ===Segmentation===<br /> {{main|Time-series segmentation}}<br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using [[Change detection|change-point detection]], or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> <br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using change-point detection, or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> = = = 分割 = = 将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。在时间序列分割中，目标是识别时间序列中的分段边界点，并刻画每个分段的动态特性。人们可以通过变点检测来解决这个问题，或者将时间序列建模为一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ==Models==<br /> <br /> ==Models==<br /> <br /> = = 模型 = = <br /> <br /> Models for time series data can have many forms and represent different [[stochastic processes]]. When modeling variations in the level of a process, three broad classes of practical importance are the ''[[autoregressive]]'' (AR) models, the ''integrated'' (I) models, and the ''[[moving average model|moving average]]'' (MA) models. These three classes depend linearly on previous data points.<ref name="linear time series">{{cite book |author-link=Neil Gershenfeld |last=Gershenfeld |first=N. |year=1999 |title=The Nature of Mathematical Modeling |url=https://archive.org/details/naturemathematic00gers_334 |url-access=limited |location=New York |publisher=Cambridge University Press |pages=[https://archive.org/details/naturemathematic00gers_334/page/n206 205]–208 |isbn=978-0521570954 }}</ref> Combinations of these ideas produce [[autoregressive moving average]] (ARMA) and [[autoregressive integrated moving average]] (ARIMA) models. The [[autoregressive fractionally integrated moving average]] (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for [[vector autoregression]]. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> Models for time series data can have many forms and represent different stochastic processes. When modeling variations in the level of a process, three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. These three classes depend linearly on previous data points. Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models. The autoregressive fractionally integrated moving average (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector autoregression. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> 时间序列数据的模型可以有多种形式，表示不同的随机过程。在对过程层次的变化进行建模时，三大类实际的重要性是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个类线性地依赖于以前的数据点。这些想法的结合产生了自回归移动平均(ARMA)和 ARIMA模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对前三种模型进行了推广。处理矢量值数据的这些类的扩展可以在多元时间序列模型的标题下得到，有时前面的首字母缩略词被扩展，包括一个初始的“ v”代表“矢量”，如在 VAR 代表向量自回归模型。这些模型的另外一组扩展可用于观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应) : 与多变量情况的区别在于强迫序列可能是确定的或者在实验者的控制之下。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a [[chaos theory|chaotic]] time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in [[nonlinear autoregressive exogenous model]]s. Further references on nonlinear time series analysis: (Kantz and Schreiber),<ref>{{cite book|last1=Kantz|first1=Holger|last2=Thomas|first2=Schreiber|title=Nonlinear Time Series Analysis|date=2004|publisher=Cambridge University Press|location=London|isbn=978-0521529020}}</ref> and (Abarbanel)<ref>{{cite book|last1=Abarbanel|first1=Henry|title=Analysis of Observed Chaotic Data|date=Nov 25, 1997|publisher=Springer|location=New York|isbn=978-0387983721}}</ref><br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a chaotic time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in nonlinear autoregressive exogenous models. Further references on nonlinear time series analysis: (Kantz and Schreiber), and (Abarbanel)<br /> <br /> 一系列数据的水平对以前的数据点的非线性依赖是有趣的，部分是因为产生混沌时间序列的可能性。然而，更重要的是，经验调查可以表明使用来自非线性模型的预测优于来自线性模型的预测，例如在非线性自回归外生模型中。非线性时间序列分析的进一步参考文献: (Kantz 和 Schreiber)和(Abarbanel) <br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time ([[heteroskedasticity]]). These models represent [[autoregressive conditional heteroskedasticity]] (ARCH) and the collection comprises a wide variety of representation ([[GARCH]], TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a [[doubly stochastic model]].<br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time (heteroskedasticity). These models represent autoregressive conditional heteroskedasticity (ARCH) and the collection comprises a wide variety of representation (GARCH, TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a doubly stochastic model.<br /> <br /> 在其他类型的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型代表了 ARCH模型(ARCH) ，收藏包括各种各样的代表(GARCH，TARCH，EGARCH，FIGARCH，CGARCH 等等)。在这里，变异性的变化与观测系列的最近过去的值有关，或者是预测的。这与局部变化的其他可能表现形式形成对比，在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also [[Markov switching multifractal]] (MSMF) techniques for modeling volatility evolution.<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution.<br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列，试图说明在多个尺度上的时间依赖。参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> A [[Hidden Markov model]] (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest [[dynamic Bayesian network]]. HMM models are widely used in [[speech recognition]], for translating a time series of spoken words into text.<br /> <br /> A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.<br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔科姆可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，用于将语音序列转换成文本。<br /> <br /> ===Notation===<br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series ''X'' that is indexed by the [[natural number]]s is written<br /> :''X'' = (''X''<sub>1</sub>, ''X''<sub>2</sub>, ...).<br /> <br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written<br /> :X = (X1, X2, ...).<br /> <br /> = = = 表示法 = = 用于时间序列分析的许多不同的表示法。一个用于指定时间序列 x 的通用符号是: x = (X1，X2，...)。<br /> <br /> Another common notation is<br /> :''Y'' = (''Y<sub>t</sub>'': ''t'' ∈ ''T''),<br /> where ''T'' is the [[index set]].<br /> <br /> Another common notation is<br /> :Y = (Yt: t ∈ T),<br /> where T is the index set.<br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===Conditions===<br /> There are two sets of conditions under which much of the theory is built:<br /> * [[Stationary process]]<br /> * [[Ergodic process]]<br /> <br /> There are two sets of conditions under which much of the theory is built:<br /> * Stationary process<br /> * Ergodic process<br /> <br /> 这个理论的大部分建立在两个条件之下: <br /> * 平稳过程遍历过程<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: [[strict stationarity]] and [[Stationary process#Weaker forms of stationarity|second-order stationarity]]. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: strict stationarity and second-order stationarity. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> 然而，平稳性的概念必须扩展到考虑两个重要的概念: 严格平稳性和二阶平稳性。模型和应用程序都可以在这些条件中的每一种情况下开发，尽管后一种情况下的模型可能被认为只是部分具体说明。<br /> <br /> In addition, time-series analysis can be applied where the series are [[Cyclostationary process|seasonally stationary]] or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in [[time-frequency analysis]] which makes use of a [[time–frequency representation]] of a time-series or signal.<ref>Boashash, B. (ed.), (2003) ''Time-Frequency Signal Analysis and Processing: A Comprehensive Reference'', Elsevier Science, Oxford, 2003 {{isbn|0-08-044335-4}}</ref><br /> <br /> In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.Boashash, B. (ed.), (2003) Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003 <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或非平稳的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。波阿什，b。我不知道你在说什么。) ，(2003)《时频信号分析与处理: 综合参考》，爱思唯尔科学出版社，牛津，2003<br /> <br /> ===Tools===<br /> Tools for investigating time-series data include:<br /> <br /> Tools for investigating time-series data include:<br /> <br /> = = = 调查时间序列数据的工具包括:<br /> <br /> * Consideration of the [[autocorrelation|autocorrelation function]] and the [[Spectral density|spectral density function]] (also [[cross-correlation function]]s and cross-spectral density functions)<br /> * [[Scaled correlation|Scaled]] cross- and auto-correlation functions to remove contributions of slow components<ref name="Nikolicetal">{{cite journal |last1=Nikolić |first1=D. |last2=Muresan |first2=R. C. |last3=Feng |first3=W. |last4=Singer |first4=W. |year=2012 |title=Scaled correlation analysis: a better way to compute a cross-correlogram |journal=European Journal of Neuroscience |volume=35 |issue=5 |pages=742–762 |doi=10.1111/j.1460-9568.2011.07987.x |pmid=22324876 |s2cid=4694570 |url=https://semanticscholar.org/paper/caa784fc3c22656413143559c402b54d0567f4d1 }}</ref><br /> * Performing a [[Fourier transform]] to investigate the series in the [[frequency domain]]<br /> * Use of a [[digital filter|filter]] to remove unwanted [[noise (physics)|noise]]<br /> * [[Principal component analysis]] (or [[empirical orthogonal function]] analysis)<br /> * [[Singular spectrum analysis]]<br /> * "Structural" models:<br /> ** General [[State Space Model]]s<br /> ** Unobserved Components Models<br /> * [[Machine Learning]]<br /> ** [[Artificial neural network]]s<br /> ** [[Support vector machine]]<br /> ** [[Fuzzy logic]]<br /> ** [[Gaussian process]]<br /> ** [[Genetic Programming]]<br /> ** [[Gene expression programming]]<br /> ** [[Hidden Markov model]]<br /> ** [[Multi expression programming]]<br /> * [[Queueing theory]] analysis<br /> * [[Control chart]]<br /> ** [[Shewhart individuals control chart]]<br /> ** [[CUSUM]] chart<br /> ** [[EWMA chart]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Nonlinear mixed-effects model|Nonlinear mixed-effects modeling]]<br /> * [[Dynamic time warping]]<ref name="Sakoe 1978">{{cite book |last1=Sakoe |first1=Hiroaki |last2=Chiba |first2=Seibi |year=1978 |chapter=Dynamic programming algorithm optimization for spoken word recognition |volume=26 |pages=43–49 |doi=10.1109/TASSP.1978.1163055 |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |s2cid=17900407 |chapter-url=https://semanticscholar.org/paper/18f355d7ef4aa9f82bf5c00f84e46714efa5fd77 }}</ref><br /> * [[Cross-correlation]]<ref>{{cite book |last1=Goutte |first1=Cyril |last2=Toft |first2=Peter |last3=Rostrup |first3=Egill |last4=Nielsen |first4=Finn Å. |last5=Hansen |first5=Lars Kai |year=1999 |chapter=On Clustering fMRI Time Series |volume=9 |issue=3 |pages=298–310 |doi=10.1006/nimg.1998.0391 |pmid=10075900 |journal=NeuroImage |s2cid=14147564 |chapter-url=https://semanticscholar.org/paper/2d5c663fb53d8348bdf3c4df0f881b5db2dcf5e3 }}</ref><br /> * [[Dynamic Bayesian network]]<br /> * [[Time-frequency representation|Time-frequency analysis techniques:]]<br /> ** [[Fast Fourier transform]]<br /> ** [[Continuous wavelet transform]]<br /> ** [[Short-time Fourier transform]]<br /> ** [[Chirplet transform]]<br /> ** [[Fractional Fourier transform]]<br /> * [[Chaos theory|Chaotic analysis]]<br /> ** [[Correlation dimension]]<br /> ** [[Recurrence plot]]s<br /> ** [[Recurrence quantification analysis]]<br /> ** [[Lyapunov exponent]]s<br /> ** [[Entropy encoding]]<br /> <br /> * Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions)<br /> * Scaled cross- and auto-correlation functions to remove contributions of slow components<br /> * Performing a Fourier transform to investigate the series in the frequency domain<br /> * Use of a filter to remove unwanted noise<br /> * Principal component analysis (or empirical orthogonal function analysis)<br /> * Singular spectrum analysis<br /> * "Structural" models:<br /> ** General State Space Models<br /> ** Unobserved Components Models<br /> * Machine Learning<br /> ** Artificial neural networks<br /> ** Support vector machine<br /> ** Fuzzy logic<br /> ** Gaussian process<br /> ** Genetic Programming<br /> ** Gene expression programming<br /> ** Hidden Markov model<br /> ** Multi expression programming<br /> * Queueing theory analysis<br /> * Control chart<br /> ** Shewhart individuals control chart<br /> ** CUSUM chart<br /> ** EWMA chart<br /> * Detrended fluctuation analysis<br /> * Nonlinear mixed-effects modeling<br /> * Dynamic time warping<br /> * Cross-correlation<br /> * Dynamic Bayesian network<br /> * Time-frequency analysis techniques:<br /> ** Fast Fourier transform<br /> ** Continuous wavelet transform<br /> ** Short-time Fourier transform<br /> ** Chirplet transform<br /> ** Fractional Fourier transform<br /> * Chaotic analysis<br /> ** Correlation dimension<br /> ** Recurrence plots<br /> ** Recurrence quantification analysis<br /> ** Lyapunov exponents<br /> ** Entropy encoding<br /> <br /> <br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数) <br /> * 调整互相关函数和自相关函数以去除慢分量的贡献 <br /> * 在频域中执行一个傅里叶变换来调查这个序列 <br /> * 使用<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图 <br /> * <br /> * EWMA 图 <br /> * 非趋势波动分析 <br /> * 非线性混合效应建模 <br /> * <br /> * 动态时间规整互相关 <br /> * <br /> * 动态贝氏网路 <br /> * 时频分析技术: <br /> * <br /> * 快速傅里叶变换连续小波转换 <br /> * <br /> * 短时距傅里叶变换 <br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析 <br /> * <br /> * <br /> * 复发图 <br /> * <br /> * 递归量化分析 <br /> * <br /> * Lyapunov 指数 <br /> * <br /> * <br /> * <br /> * <br /> <br /> ===Measures===<br /> Time series metrics or [[Features (pattern recognition)|features]] that can be used for time series [[Classification (machine learning)|classification]] or [[regression analysis]]:<ref>{{cite journal |last1=Mormann |first1=Florian |last2=Andrzejak |first2=Ralph G. |last3=Elger |first3=Christian E. |last4=Lehnertz |first4=Klaus |title=Seizure prediction: the long and winding road |journal=[[Brain (journal)|Brain]] |year=2007 |volume=130 |issue=2 |pages=314–333 |doi=10.1093/brain/awl241 |pmid=17008335|doi-access=free }}</ref><br /> <br /> Time series metrics or features that can be used for time series classification or regression analysis:<br /> <br /> = = = = 可用于时间序列分类或回归分析的时间序列度量或特征:<br /> <br /> * '''Univariate linear measures'''<br /> ** [[Moment (mathematics)]]<br /> ** [[Spectral band power]]<br /> ** [[Spectral edge frequency]]<br /> ** Accumulated [[Energy (signal processing)]]<br /> ** Characteristics of the [[autocorrelation]] function<br /> ** [[Hjorth parameters]]<br /> ** [[Fast Fourier transform|FFT]] parameters<br /> ** [[Autoregressive model]] parameters<br /> ** [[Mann–Kendall test]]<br /> * '''Univariate non-linear measures'''<br /> ** Measures based on the [[correlation]] sum<br /> ** [[Correlation dimension]]<br /> ** [[Correlation integral]]<br /> ** [[Correlation density]]<br /> ** [[Correlation entropy]]<br /> ** [[Approximate entropy]]<ref>{{cite web |last1=Land |first1=Bruce |last2=Elias |first2=Damian |title=Measuring the 'Complexity' of a time series |url=http://www.nbb.cornell.edu/neurobio/land/PROJECTS/Complexity/ }}</ref><br /> ** [[Sample entropy]]<br /> ** {{iw2|Fourier entropy||uk|Ентропія Фур'є}}<br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** [[Rényi entropy]]<br /> ** Higher-order methods<br /> ** [[Marginal predictability]]<br /> ** [[Dynamical similarity]] index<br /> ** [[State space]] dissimilarity measures<br /> ** [[Lyapunov exponent]]<br /> ** Permutation methods<br /> ** [[Local flow]]<br /> * '''Other univariate measures'''<br /> ** [[Algorithmic information theory|Algorithmic complexity]]<br /> ** [[Kolmogorov complexity]] estimates<br /> ** [[Hidden Markov Model]] states<br /> ** [[Rough path#Signature|Rough path signature]]<ref>[1] Chevyrev, I., Kormilitzin, A. (2016) "[https://arxiv.org/abs/1603.03788 A Primer on the Signature Method in Machine Learning], arXiv:1603.03788v1"</ref><br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * '''Bivariate linear measures'''<br /> ** Maximum linear [[cross-correlation]]<br /> ** Linear [[Coherence (signal processing)]]<br /> * '''Bivariate non-linear measures'''<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for [[Phase synchronization]]<br /> ** Measures for [[Phase locking]]<br /> * '''Similarity measures''':<ref>{{cite journal |last1=Ropella |first1=G. E. P. |last2=Nag |first2=D. A. |last3=Hunt |first3=C. A. |title=Similarity measures for automated comparison of in silico and in vitro experimental results |journal=Engineering in Medicine and Biology Society |year=2003 |volume=3 |pages=2933–2936 |doi=10.1109/IEMBS.2003.1280532 |isbn=978-0-7803-7789-9 |s2cid=17798157 }}</ref><br /> ** [[Cross-correlation]]<br /> ** [[Dynamic Time Warping]]<ref name="Sakoe 1978"/><br /> ** [[Hidden Markov Models]]<br /> ** [[Edit distance]]<br /> ** [[Total correlation]]<br /> ** [[Newey–West estimator]]<br /> ** [[Prais–Winsten estimation|Prais–Winsten transformation]]<br /> ** Data as Vectors in a Metrizable Space<br /> *** [[Minkowski distance]]<br /> *** [[Mahalanobis distance]]<br /> ** Data as time series with envelopes<br /> *** Global [[standard deviation]]<br /> *** Local [[standard deviation]]<br /> *** Windowed [[standard deviation]]<br /> ** Data interpreted as stochastic series<br /> *** [[Pearson product-moment correlation coefficient]]<br /> *** [[Spearman's rank correlation coefficient]]<br /> ** Data interpreted as a [[probability distribution]] function<br /> *** [[Kolmogorov–Smirnov test]]<br /> *** [[Cramér–von Mises criterion]]<br /> <br /> * Univariate linear measures<br /> ** Moment (mathematics)<br /> ** Spectral band power<br /> ** Spectral edge frequency<br /> ** Accumulated Energy (signal processing)<br /> ** Characteristics of the autocorrelation function<br /> ** Hjorth parameters<br /> ** FFT parameters<br /> ** Autoregressive model parameters<br /> ** Mann–Kendall test<br /> * Univariate non-linear measures<br /> ** Measures based on the correlation sum<br /> ** Correlation dimension<br /> ** Correlation integral<br /> ** Correlation density<br /> ** Correlation entropy<br /> ** Approximate entropy<br /> ** Sample entropy<br /> ** <br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** Rényi entropy<br /> ** Higher-order methods<br /> ** Marginal predictability<br /> ** Dynamical similarity index<br /> ** State space dissimilarity measures<br /> ** Lyapunov exponent<br /> ** Permutation methods<br /> ** Local flow<br /> * Other univariate measures<br /> ** Algorithmic complexity<br /> ** Kolmogorov complexity estimates<br /> ** Hidden Markov Model states<br /> ** Rough path signature[1] Chevyrev, I., Kormilitzin, A. (2016) "A Primer on the Signature Method in Machine Learning, arXiv:1603.03788v1"<br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * Bivariate linear measures<br /> ** Maximum linear cross-correlation<br /> ** Linear Coherence (signal processing)<br /> * Bivariate non-linear measures<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for Phase synchronization<br /> ** Measures for Phase locking<br /> * Similarity measures:<br /> ** Cross-correlation<br /> ** Dynamic Time Warping<br /> ** Hidden Markov Models<br /> ** Edit distance<br /> ** Total correlation<br /> ** Newey–West estimator<br /> ** Prais–Winsten transformation<br /> ** Data as Vectors in a Metrizable Space<br /> *** Minkowski distance<br /> *** Mahalanobis distance<br /> ** Data as time series with envelopes<br /> *** Global standard deviation<br /> *** Local standard deviation<br /> *** Windowed standard deviation<br /> ** Data interpreted as stochastic series<br /> *** Pearson product-moment correlation coefficient<br /> *** Spearman's rank correlation coefficient<br /> ** Data interpreted as a probability distribution function<br /> *** Kolmogorov–Smirnov test<br /> *** Cramér–von Mises criterion<br /> <br /> <br /> * 单变量线性测量 <br /> * <br /> * 矩(数学) <br /> * <br /> * 谱带功率 <br /> * <br /> * 谱边缘频率 <br /> * <br /> * 累积能量(信号处理) <br /> * <br /> * 自相关函数特性 <br /> * <br /> * Hjorth 参数 <br /> * <br /> * FFT 参数 <br /> * <br /> * 自回归模型参数 <br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流 <br /> * 其他单变量度量 <br /> * <br /> * 算法复杂度 <br /> * <br /> * 柯氏复杂性估计 <br /> * <br /> * 隐马尔可夫模型状态 <br /> * <br /> * 粗糙路径签名[1] Chevyrev，i. ，Kormilitzin，a。(2016)“ a Primer on the Signature Method in Machine Learning，arXiv: 1603.03788 v1”<br /> * <br /> * 替代时间序列和替代校正 <br /> * <br /> * 递归损失(非平稳度) <br /> * 双变量线性度量 <br /> * <br /> * 最大线性互相关 <br /> * <br /> * 线性相干性(信号处理) <br /> * 双变量非线性度量 <br /> * <br /> * 非线性相互依赖 <br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学) <br /> * <br /> * 相位同步的度量 <br /> * <br /> * 相位锁定的度量 <br /> * <br /> * 相似度量: <br /> * <br /> * 互相关 <br /> * <br /> * <br /> * 动态时间规整 <br /> * <br /> * <br /> * 隐马尔可夫模型 <br /> * <br /> * <br /> * 编辑距离 <br /> * <br /> * 总相关性 <br /> * <br /> * Newey-West 估计 <br /> * <br /> * Prais-Winsten 变换 <br /> * <br /> * 数据作为向量在乌雷松度量化定理 <br /> * <br /> * <br /> * 明氏距离 <br /> * <br /> * 马氏距离 <br /> * <br /> * 数据作为时间序列与信封 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差标准差 <br /> * <br /> * <br /> * 窗口标准差 <br /> * <br /> * 数据解释为随机序列 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数 <br /> * <br /> * 数据解释为概率分布函数 <br /> * <br /> * Kolmogorov-Smirnov 检验 <br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ==Visualization==<br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<ref>{{cite web|last1=Tominski|first1=Christian|last2= Aigner|first2=Wolfgang|title=The TimeViz Browser:A Visual Survey of Visualization Techniques for Time-Oriented Data|url=http://survey.timeviz.net/|access-date=1 June 2014}}</ref><br /> <br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<br /> <br /> = = 可视化 = = 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> ===Overlapping charts===<br /> * [[Braided graphs]]<br /> * Line charts<br /> * Slope graphs<br /> * {{iw2|GapChart||fr}}<br /> <br /> * Braided graphs<br /> * Line charts<br /> * Slope graphs<br /> * <br /> <br /> = = = = 重叠图 = = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> ===Separated charts===<br /> * [[Horizon graphs]]<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> * Horizon graphs<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> = = = = = 分离图表 = = = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ==See also==<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ==References==<br /> {{Reflist|2}}<br /> <br /> ==Further reading==<br /> * {{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> * [[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> * {{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> * {{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> * [[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]]. {{ISBN|978-0-12-564901-8}}<br /> * {{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer, {{ISBN|978-3-319-52451-1}}<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> * [[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> * {{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> = = 进一步阅读 = = <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社。<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社。<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去。北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社。<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社。<br /> *<br /> <br /> ==External links==<br /> {{Commons category}}<br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> <br /> *Introduction to Time series Analysis (Engineering Statistics Handbook) — A practical guide to Time series analysis.<br /> <br /> = = 外部链接 = = <br /> * 时间序列分析导论(工程统计手册)ー时间序列分析实用指南。<br /> <br /> {{Statistics}}<br /> {{Portal bar|Mathematics}}<br /> {{Authority control}}<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> <br /> <br /> <br /> Category:Statistical data types<br /> Category:Mathematical and quantitative methods (economics)<br /> Category:Machine learning<br /> <br /> 类别: 统计数据类型类别: 数学和定量方法(经济学)类别: 机器学习<br /> <br /> <noinclude><br /> <br /> <small>This page was moved from [[wikipedia:en:Time series]]. Its edit history can be viewed at [[时间序列分析/edithistory]]</small></noinclude><br /> <br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E6%97%B6%E9%97%B4%E5%BA%8F%E5%88%97%E5%88%86%E6%9E%90&diff=33943 时间序列分析 2023-01-31T13:03:24Z

<p>TYcl20：</p> <hr /> <div><br /> {{short description|Sequence of data points over time}}<br /> [[File:Random-data-plus-trend-r2.png|thumb|250px|Time series: random data plus trend, with best-fit line and different applied filters时间序列：随机数据加趋势，带有最佳拟合线和不同的过滤器|right|链接=Special:FilePath/Random-data-plus-trend-r2.png]]<br /> In [[mathematics]], a '''time series''' is a series of [[data point]]s indexed (or listed or graphed) in time order. A time series is a [[sequence]] taken at successive equally spaced points in time. Thus it is a sequence of [[discrete-time]] data. Examples of time series are heights of ocean [[tides]], counts of [[sunspots]], and the daily closing value of the [[Dow Jones Industrial Average]].<br /> <br /> 数学中的时间序列是指按时间顺序索引(或列出或绘制)的一系列数据点。时间序列是在连续的等距时间点上的序列。因此，这种序列上的时间是处于离散状态的。测量海洋潮汐的高度、计算太阳黑子的数量和分析道琼斯工业平均指数的每日收盘价都是时间序列在实际工作上的应用。<br /> <br /> <br /> <br /> A Time series is very frequently plotted via a [[run chart]] (which is a temporal [[line chart]]). Time series are used in [[statistics]], [[signal processing]], [[pattern recognition]], [[econometrics]], [[mathematical finance]], [[weather forecasting]], [[earthquake prediction]], [[electroencephalography]], [[control engineering]], [[astronomy]], [[communications engineering]], and largely in any domain of applied [[Applied science|science]] and [[engineering]] which involves [[Time|temporal]] measurements.<br /> <br /> 时间序列常通过趋势图（即时间线图Line chart）具象化。时间序列常被用于统计学、信号处理、模式识别、计量经济学、数理金融学、天气预报、地震预测、脑电图、控制工程、天文学、通信工程，以及涉及时序测量的任何科学和工程领域。<br /> <br /> <br /> '''Time series ''analysis''''' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. '''Time series ''forecasting''''' is the use of a [[model (abstract)|model]] to predict future values based on previously observed values. While [[regression analysis]] is often employed in such a way as to test relationships between one or more different time series, this type of analysis is not usually called "time series analysis", which refers in particular to relationships between different points in time within a single series. [[Interrupted time series]] analysis is used to detect changes in the evolution of a time series from before to after some intervention which may affect the underlying variable.<br /> <br /> 时间序列分析Time series analysis包含了以提取时间序列数据中有意义的统计特征和数据的其他特征为目的的方法。时间序列预测Time series forecasting是基于先前观测到的值，使用模型Model来预测未来值的方法。虽然回归分析Regression analysis经常被用于分析一个或多个不同时间序列之间的关系，但这种类型的分析通常不被称为 "时间序列分析"。时间序列分析特指的是分析单一序列中不同时间点之间的关系。中断时间序列Interrupted time series分析是用来检测时间序列在接受干预前后的变化，这种干预可能会影响基础变量。<br /> <br /> <br /> Time series data have a natural temporal ordering. This makes time series analysis distinct from [[cross-sectional study|cross-sectional studies]], in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from [[spatial data analysis]] where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A [[stochastic]] model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see [[time reversibility]]).<br /> <br /> 时间序列数据具有自然的时间排序。这使得时间序列分析有别于截面研究Cross-sectional studies，在截面研究中，观察结果没有自然排序（例如，通过参考各自的教育水平来解释人们的工资，其中个人的数据可以按任何顺序输入）。时间序列分析也有别于空间数据分析Spatial data analysis，后者的观测值通常与地理位置有关（例如，通过地点以及房屋的内在特征来说明房价）。时间序列的随机Stochastic模型通常会反映这样一个事实，即在时间上相距较近的观测值会比相距较远的观测值更密切相关。此外，时间序列模型通常会利用自然的单向时间顺序，以便将给定时间段的值表示为以某种方式从过去的值而不是从未来的值中得出（参见时间可逆性Time reversibility）。<br /> <br /> <br /> Time series analysis can be applied to [[real number|real-valued]], continuous data, [[:wikt:discrete|discrete]] [[Data type#Numeric types|numeric]] data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the [[English language]]<ref name=":0">{{cite book |last1=Lin |first1=Jessica |last2=Keogh |first2=Eamonn |last3=Lonardi |first3=Stefano |last4=Chiu |first4=Bill |chapter=A symbolic representation of time series, with implications for streaming algorithms |title=Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery |pages=2–11 |year=2003 |location=New York |publisher=ACM Press |doi=10.1145/882082.882086|citeseerx=10.1.1.14.5597 |s2cid=6084733 }}</ref>).<br /> <br /> <br /> 时间序列分析可以应用于实值、连续数据、离散数值Numeric数据或离散符号数据（即字符序列，如英语English language中的字母和单词<ref name=":0" />）。<br /> <br /> ==Methods for analysis分析方法==<br /> Methods for time series analysis may be divided into two classes: [[frequency-domain]] methods and [[time-domain]] methods. The former include [[frequency spectrum#Spectrum analysis|spectral analysis]] and [[wavelet analysis]]; the latter include [[auto-correlation]] and [[cross-correlation]] analysis. In the time domain, correlation and analysis can be made in a filter-like manner using [[scaled correlation]], thereby mitigating the need to operate in the frequency domain.<br /> <br /> 时间序列分析的方法可分为两类：频域Frequency-domain方法和时域Time-domain方法。前者包括频谱分析Spectral analysis和小波分析Wavelet analysis；后者包括自相关Auto-correlation和交叉相关Cross-correlation analysis分析。在时域中，可以用类似于滤波器的方式使用标度相关性Scaled correlation来进行关联和分析，从而减轻了在频域中操作的需要。<br /> <br /> <br /> Additionally, time series analysis techniques may be divided into [[Parametric estimation|parametric]] and [[Non-parametric statistics|non-parametric]] methods. The [[Parametric estimation|parametric approaches]] assume that the underlying [[stationary process|stationary stochastic process]] has a certain structure which can be described using a small number of parameters (for example, using an [[autoregressive]] or [[moving average model]]). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, [[Non-parametric statistics|non-parametric approaches]] explicitly estimate the [[covariance]] or the [[spectrum]] of the process without assuming that the process has any particular structure.<br /> <br /> 此外，时间序列分析技术可分为参数化Parametric和非参数化Non-parametric方法。参数方法Parametric approaches假定基础的平稳随机过程Stationary stochastic process具有某种结构，可以用少量的参数来描述（例如，使用自回归Autoregressive或移动平均模型Moving average model）。在这些方法中，任务是估计描述随机过程的模型的参数。相比之下，非参数方法Non-parametric approaches明确地估计过程的协方差Covariance或频谱Spectrum，而不假设过程有任何特定的结构。<br /> <br /> <br /> Methods of time series analysis may also be divided into [[Linear regression|linear]] and [[Nonlinear regression|non-linear]], and [[Univariate analysis|univariate]] and [[Multivariate analysis|multivariate]].<br /> <br /> 时间序列分析的方法也可以分为线性Linear 和非线性Non-linear，以及单变量Univariate 和多变量Multivariate。<br /> <br /> ==Panel data面板数据==<br /> A time series is one type of [[panel data]]. Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a [[cross-sectional data]]set). A data set may exhibit characteristics of both panel data and time series data. One way to tell is to ask what makes one data record unique from the other records. If the answer is the time data field, then this is a time series data set candidate. If determining a unique record requires a time data field and an additional identifier which is unrelated to time (e.g. student ID, stock symbol, country code), then it is panel data candidate. If the differentiation lies on the non-time identifier, then the data set is a cross-sectional data set candidate.<br /> <br /> 时间序列是面板数据Panel data的一种类型，面板数据是更大的类别。面板数据是一个多维的数据集，而时间序列数据集是一个一维的面板（正如截面数据Cross-sectional data集一样）。一个数据集可能同时表现出面板数据和时间序列数据的特征。判断的方法之一是探究是什么使一条数据记录与其他记录不同。如果答案是时间数据字段，那么这就是一个时间序列数据集候选。如果确定一个独特的记录需要一个时间数据字段和一个与时间无关的额外标识符（如学生证、股票代码、国家代码），那么它就是面板数据的候选。如果区别在于非时间标识符，那么该数据集就是一个截面数据集候选。<br /> <br /> ==Analysis分析==<br /> There are several types of motivation and data analysis available for time series which are appropriate for different purposes.<br /> <br /> 对于具有不同目的的时间序列，适用的动机和数据分析方法都不同。<br /> <br /> ===Motivation动机===<br /> In the context of [[statistics]], [[econometrics]], [[quantitative finance]], [[seismology]], [[meteorology]], and [[geophysics]] the primary goal of time series analysis is [[forecasting]]. In the context of [[signal processing]], [[control engineering]] and [[communication engineering]] it is used for signal detection. Other applications are in [[data mining]], [[pattern recognition]] and [[machine learning]], where time series analysis can be used for [[cluster analysis|clustering]],<ref name=":1">{{cite journal | last1 = Liao | first1 = T. Warren | title = Clustering of time series data - a survey | journal = Pattern Recognition | volume = 38 | issue = 11 | pages = 1857–1874 | publisher = Elsevier | date = 2005 | language = en | doi = 10.1016/j.patcog.2005.01.025| bibcode = 2005PatRe..38.1857W }}{{subscription required|via=ScienceDirect }}</ref><ref name=":2">{{cite journal | last1 = Aghabozorgi | first1 = Saeed | last2 = Shirkhorshidi | first2 = Ali S. | last3 = Wah | first3 = Teh Y. | title = Time-series clustering – A decade review | journal = Information Systems | volume = 53 | pages = 16–38 | publisher = Elsevier | date = 2015 | language = en | doi = 10.1016/j.is.2015.04.007}}{{subscription required|via=ScienceDirect }}</ref> [[Statistical classification|classification]],<ref name=":3">{{cite journal | last1 = Keogh | first1 = Eamonn J. | title = On the need for time series data mining benchmarks | journal = Data Mining and Knowledge Discovery | volume = 7 | pages = 349–371 | publisher = Kluwer | date = 2003 | language = en | doi = 10.1145/775047.775062| isbn = 158113567X | s2cid = 41617550 }}{{subscription required|via=ACM Digital Library }}</ref> query by content,<ref name=":4">{{cite conference|last1=Agrawal|first1=Rakesh|last2=Faloutsos|first2=Christos|last3=Swami|first3=Arun|date=October 1993|title=Efficient Similarity Search In Sequence Databases|conference=International Conference on Foundations of Data Organization and Algorithms|volume=730|pages=69–84|book-title=Proceedings of the 4th International Conference on Foundations of Data Organization and Algorithms|doi=10.1007/3-540-57301-1_5}}{{Subscription required|via=SpringerLink}}</ref> [[anomaly detection]] as well as [[forecasting]].<ref name=":5">{{cite journal|last1=Chen|first1=Cathy W. S.|last2=Chiu|first2=L. M.|date=September 2021|title=Ordinal Time Series Forecasting of the Air Quality Index|journal=Entropy|language=en|volume=23|issue=9|pages=1167|doi=10.3390/e23091167|pmid=34573792|pmc=8469594|bibcode=2021Entrp..23.1167C|doi-access=free}}</ref><br /> <br /> 在统计学Statistics、计量经济学Econometrics、定量金融学Quantitative finance、地震学Seismology、气象学Meteorology和地球物理学Geophysics方面，时间序列分析的主要目标是预测Forecasting。在信号处理Signal processing、控制工程Control engineering和通信工程Communication engineering方面，它被用于信号检测。在数据挖掘Data mining、模式识别Pattern recognition和机器学习Machine learning等其他应用中，时间序列分析可用于聚类Clustering<ref name=":1" /><ref name=":2" />、分类Classification<ref name=":3" />、按内容查询<ref name=":4" />、异常检测Anomaly detection以及预测Forecasting<ref name=":5" />。<br /> <br /> ===Exploratory analysis探索性分析===<br /> [[File:Tuberculosis incidence US 1953-2009.png|thumb|Tuberculosis incidence US 1953-2009美国1953-2009年结核病发病率|链接=Special:FilePath/Tuberculosis_incidence_US_1953-2009.png]]<br /> {{further|Exploratory analysis}}<br /> A straightforward way to examine a regular time series is manually with a [[line chart]]. An example chart is shown on the right for tuberculosis incidence in the United States, made with a spreadsheet program. The number of cases was standardized to a rate per 100,000 and the percent change per year in this rate was calculated. The nearly steadily dropping line shows that the TB incidence was decreasing in most years, but the percent change in this rate varied by as much as +/- 10%, with 'surges' in 1975 and around the early 1990s. The use of both vertical axes allows the comparison of two time series in one graphic.<br /> <br /> 绘制折线图Line chart是检查常规时间序列的直观方法。右侧显示了一个使用电子表格程序制作的美国结核病发病率示例图表。病例的数量被标准化为每10万人的比率，并计算出该比率每年的变化百分比。几乎稳定下降的线条表明，结核病发病率在大多数年份都在下降，但该比率的变化百分比高达+/-10%，在1975年和20世纪90年代初前后出现了 "激增"。图中应用了两个纵轴，使得可以在一个图表中比较两个时间序列。<br /> <br /> <br /> A study of corporate data analysts found two challenges to exploratory time series analysis: discovering the shape of interesting patterns, and finding an explanation for these patterns.<ref name=":6">{{Cite journal|last=Sarkar|first=Advait|last2=Spott|first2=Martin|last3=Blackwell|first3=Alan F.|last4=Jamnik|first4=Mateja|date=2016|title=Visual discovery and model-driven explanation of time series patterns|url=https://doi.org/10.1109/VLHCC.2016.7739668|journal=2016 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)|publisher=IEEE|doi=10.1109/vlhcc.2016.7739668}}</ref> Visual tools that represent time series data as [[Heat map|heat map matrices]] can help overcome these challenges.<br /> <br /> 一项对企业数据分析师的研究发现，探索性时间序列分析有两个挑战：发现有趣模式，以及为这些模式找到解释<ref name=":6" />。将时间序列数据可视化为热力图矩阵Heat map matrices的工具可以帮助克服这些挑战。<br /> <br /> <br /> Other techniques include:<br /> <br /> 其他技巧包括:<br /> <br /> * [[Autocorrelation]] analysis to examine [[serial dependence]]<br /> * [[frequency spectrum#Spectrum analysis|Spectral analysis]] to examine cyclic behavior which need not be related to [[seasonality]]. For example, sunspot activity varies over 11 year cycles.<ref>{{cite book |last=Bloomfield |first=P. |year=1976 |title=Fourier analysis of time series: An introduction |location=New York |publisher=Wiley |isbn=978-0471082569 }}</ref><ref>{{cite book |last=Shumway |first=R. H. |year=1988 |title=Applied statistical time series analysis |location=Englewood Cliffs, NJ |publisher=Prentice Hall |isbn=978-0130415004 }}</ref> Other common examples include celestial phenomena, weather patterns, neural activity, commodity prices, and economic activity.<br /> * Separation into components representing trend, seasonality, slow and fast variation, and cyclical irregularity: see [[trend estimation]] and [[decomposition of time series]]<br /> <br /> * 自相关分析检验序列相关性；<br /> * 频谱分析来检查与季节性无关的周期性行为。例如，太阳黑子活动在一个周期内（11年）的变化。其他常见的例子包括天体现象、天气模式、神经活动、商品价格和经济活动；<br /> * 将序列分离为代表趋势、季节性、慢速和快速变化以及周期性不规则的成分：见趋势估计和时间序列的分。<br /> <br /> ===Curve fitting曲线拟合===<br /> {{main|Curve fitting}}<br /> <br /> Curve fitting<ref name=":7">Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.</ref><ref name=":8">William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.</ref> is the process of constructing a [[curve]], or [[function (mathematics)|mathematical function]], that has the best fit to a series of [[data]] points,<ref name=":9">S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. {{isbn|0306439972}} Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)</ref> possibly subject to constraints.<ref name=":10">[https://archive.org/details/signalnoisewhymo00silv]''[[The Signal and the Noise]]'': Why So Many Predictions Fail-but Some Don't.'' By Nate Silver''</ref><ref name=":11">[https://books.google.com/books?id=hhdVr9F-JfAC Data Preparation for Data Mining]: Text. By Dorian Pyle.</ref> Curve fitting can involve either [[interpolation]],<ref name=":12">Numerical Methods in Engineering with MATLAB®. By [[Jaan Kiusalaas]]. Page 24.</ref><ref name=":13">[https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false Numerical Methods in Engineering with Python 3]. By Jaan Kiusalaas. Page 21.</ref> where an exact fit to the data is required, or [[smoothing]],<ref name=":14">[https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false Numerical Methods of Curve Fitting]. By P. G. Guest, Philip George Guest. Page 349.</ref><ref name=":15">See also: [[Mollifier]]</ref> in which a "smooth" function is constructed that approximately fits the data. A related topic is [[regression analysis]],<ref name=":16">[http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf Fitting Models to Biological Data Using Linear and Nonlinear Regression]. By Harvey Motulsky, Arthur Christopoulos.</ref><ref name=":17">Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.</ref> which focuses more on questions of [[statistical inference]] such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization,<ref name=":18">Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.</ref><ref name=":19">[https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false Numerical Methods for Nonlinear Engineering Models]. By John R. Hauser. Page 227.</ref> to infer values of a function where no data are available,<ref name=":20">Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.</ref> and to summarize the relationships among two or more variables.<ref name=":21">Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.</ref> [[Extrapolation]] refers to the use of a fitted curve beyond the [[range (statistics)|range]] of the observed data,<ref name=":22">[https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false Community Analysis and Planning Techniques]. By Richard E. Klosterman. Page 1.</ref> and is subject to a [[Uncertainty|degree of uncertainty]]<ref name=":23">An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. [https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69 Pg 69]</ref> since it may reflect the method used to construct the curve as much as it reflects the observed data.<br /> <br /> 正文：曲线拟合Curve fitting<br /> <br /> 曲线拟合<ref name=":7" /><ref name=":8" /> 是构建一条曲线Curve或数学函数Mathematical function的过程，它对一系列的数据Data点具有最佳的拟合效果<ref name=":9" />，可能会受到一些限制<ref name=":10" /><ref name=":11" />。曲线拟合包括插值Interpolation<ref name=":12" /><ref name=":13" />（需要精确地拟合数据）与平滑Smoothing<ref name=":14" /><ref name=":15" />（构造一个 "平滑 "的函数来近似地拟合数据）。与曲线拟合相近的回归分析Regression analysis<ref name=":16" /><ref name=":17" />更侧重于统计推断Statistical inference的问题。例如，在拟合有随机误差的数据的曲线中，有多少不确定性存在。拟合曲线可以作为数据可视化的辅助工具<ref name=":18" /><ref name=":19" />，在没有数据的情况下推断函数的值<ref name=":20" />，并总结两个或多个变量之间的关系<ref name=":21" />。外推法Extrapolation是指在观测到的数据范围Range之外使用拟合曲线<ref name=":22" />，它有一定程度的不确定性Degree of uncertainty<ref name=":23" />，因为它既可能是反映观测数据，也可能是反映用于构建曲线的方法。<br /> <br /> <br /> The construction of economic time series involves the estimation of some components for some dates by [[interpolation]] between values ("benchmarks") for earlier and later dates. Interpolation is estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from the available information ("reading between the lines").<ref name=":24">Hamming, Richard. Numerical methods for scientists and engineers. Courier Corporation, 2012.</ref> Interpolation is useful where the data surrounding the missing data is available and its trend, seasonality, and longer-term cycles are known. This is often done by using a related series known for all relevant dates.<ref name=":25">Friedman, Milton. "[http://www.nber.org/chapters/c2062.pdf The interpolation of time series by related series]." Journal of the American Statistical Association 57.300 (1962): 729–757.</ref> Alternatively [[polynomial interpolation]] or [[spline interpolation]] is used where piecewise [[polynomial]] functions are fit into time intervals such that they fit smoothly together. A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function (also called [[Polynomial regression|regression]]).The main difference between regression and interpolation is that polynomial regression gives a single polynomial that models the entire data set. Spline interpolation, however, yield a piecewise continuous function composed of many polynomials to model the data set.<br /> <br /> 经济时间序列的构建涉及通过在早期和晚期的值（“基准”）之间进行插值Interpolation来估计某些日期的某些组成部分。插值法是在两个已知量（历史数据）之间估计一个未知量，或从现有信息中得出关于缺失信息的结论（"从字里行间阅读"）<ref name=":24" />。如果围绕缺失数据的数据是可用的，并且其趋势、季节性和长期周期是已知的，那么插值法就很有用。插值法通常是通过使用已知所有相关日期的相关序列来实现的<ref name=":25" />。或者使用多项式插值Polynomial interpolation或样条插值Spline interpolation，将分段多项式Polynomial函数拟合到时间间隔中，使其平滑地拟合在一起。一个与插值密切相关的问题是用一个简单的函数来逼近一个复杂的函数（也称为回归Regression）。回归和插值的主要区别是，多项式回归给出一个单一的多项式来模拟整个数据集。而样条插值则产生一个由许多多项式组成的分段连续函数来模拟数据集。<br /> <br /> [[Extrapolation]] is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable. It is similar to [[interpolation]], which produces estimates between known observations, but extrapolation is subject to greater [[uncertainty]] and a higher risk of producing meaningless results.<br /> <br /> 外推法Extrapolation是指在原始观察范围之外，根据一个变量与另一个变量的关系来估计其数值的过程。它与插值Interpolation类似，插值在已知的观测值之间产生估计值，但外推法的不确定性Uncertainty更大，产生无意义结果的风险也更大。<br /> <br /> ===Function approximation===<br /> {{main|Function approximation}}<br /> In general, a function approximation problem asks us to select a [[function (mathematics)|function]] among a well-defined class that closely matches ("approximates") a target function in a task-specific way.<br /> One can distinguish two major classes of function approximation problems: First, for known target functions, [[approximation theory]] is the branch of [[numerical analysis]] that investigates how certain known functions (for example, [[special function]]s) can be approximated by a specific class of functions (for example, [[polynomial]]s or [[rational function]]s) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).<br /> <br /> <br /> In general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way.<br /> One can distinguish two major classes of function approximation problems: First, for known target functions, approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions) can be approximated by a specific class of functions (for example, polynomials or rational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).<br /> <br /> = = = = = = = = 一般来说，一个函数逼近问题要求我们在一个定义良好的类中选择一个函数，这个类以一种特定于任务的方式与目标函数非常匹配(“近似”)。人们可以区分两类主要的函数逼近问题: 首先，对于已知的目标函数，逼近理论是数值分析的一个分支，研究某些已知函数(例如，特殊函数)如何可以用一类特定的函数(例如，多项式或有理函数)来近似，这类函数通常具有理想的性质(廉价计算、连续性、积分和极限值等等)。).<br /> <br /> Second, the target function, call it ''g'', may be unknown; instead of an explicit formula, only a set of points (a time series) of the form (''x'', ''g''(''x'')) is provided. Depending on the structure of the [[domain of a function|domain]] and [[codomain]] of ''g'', several techniques for approximating ''g'' may be applicable. For example, if ''g'' is an operation on the [[real number]]s, techniques of [[interpolation]], [[extrapolation]], [[regression analysis]], and [[curve fitting]] can be used. If the [[codomain]] (range or target set) of ''g'' is a finite set, one is dealing with a [[statistical classification|classification]] problem instead. A related problem of ''online'' time series approximation<ref>Gandhi, Sorabh, Luca Foschini, and Subhash Suri. "[https://ieeexplore.ieee.org/abstract/document/5447930/ Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order]." Data Engineering (ICDE), 2010 IEEE 26th International Conference on. IEEE, 2010.</ref> is to summarize the data in one-pass and construct an approximate representation that can support a variety of time series queries with bounds on worst-case error.<br /> <br /> Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points (a time series) of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. If the codomain (range or target set) of g is a finite set, one is dealing with a classification problem instead. A related problem of online time series approximationGandhi, Sorabh, Luca Foschini, and Subhash Suri. "Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order." Data Engineering (ICDE), 2010 IEEE 26th International Conference on. IEEE, 2010. is to summarize the data in one-pass and construct an approximate representation that can support a variety of time series queries with bounds on worst-case error.<br /> <br /> 其次，目标函数，称为 g，可能是未知的; 代替黎曼显式公式，只有一组形式(x，g (x))的点(时间序列)被提供。根据 g 的畴和余畴的结构，几种近似 g 的方法可能是适用的。例如，如果 g 是对实数的运算，可以使用插值、外推、回归分析和曲线拟合等技术。如果 g 的余域(范围或目标集)是一个有限集，那么我们就是在处理一个分类问题。在线时间序列的一个相关问题接近于 andhi，Sorabh，Luca Foschini，和 Subhash Suri。时间序列数据的空间有效在线近似: 数据流、失忆和无序数据工程，2010年 IEEE 第26届国际会议。2010.是对数据进行一次总结，构造一个近似表示，可以支持各种时间序列查询，最坏情况下的错误界限。<br /> <br /> To some extent, the different problems ([[regression analysis|regression]], [[Statistical classification|classification]], [[fitness approximation]]) have received a unified treatment in [[statistical learning theory]], where they are viewed as [[supervised learning]] problems.<br /> <br /> To some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.<br /> <br /> 在某种程度上，不同的问题(回归、分类、适应度逼近)在统计学习理论中得到了统一的处理，它们被视为监督式学习问题。<br /> <br /> ===Prediction and forecasting===<br /> In [[statistics]], [[prediction]] is a part of [[statistical inference]]. One particular approach to such inference is known as [[predictive inference]], but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as [[forecasting]].<br /> * Fully formed statistical models for [[stochastic simulation]] purposes, so as to generate alternative versions of the time series, representing what might happen over non-specific time-periods in the future<br /> * Simple or fully formed statistical models to describe the likely outcome of the time series in the immediate future, given knowledge of the most recent outcomes (forecasting).<br /> * Forecasting on time series is usually done using automated statistical software packages and programming languages, such as [[Julia (programming language)|Julia]], [[Python (programming language)|Python]], [[R (programming language)|R]], [[SAS (software)|SAS]], [[SPSS]] and many others.<br /> * Forecasting on large scale data can be done with [[Apache Spark]] using the Spark-TS library, a third-party package.<ref>{{cite web |title=Time Series Analysis with Spark |author=Sandy Ryza |date=2020-03-18 |access-date=2021-01-12 |url=https://databricks.com/session/time-series-analysis-with-spark |format=slides of a talk at Spark Summit East 2016 |publisher=[[Databricks]]}}</ref><br /> <br /> In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as forecasting.<br /> * Fully formed statistical models for stochastic simulation purposes, so as to generate alternative versions of the time series, representing what might happen over non-specific time-periods in the future<br /> * Simple or fully formed statistical models to describe the likely outcome of the time series in the immediate future, given knowledge of the most recent outcomes (forecasting).<br /> * Forecasting on time series is usually done using automated statistical software packages and programming languages, such as Julia, Python, R, SAS, SPSS and many others.<br /> * Forecasting on large scale data can be done with Apache Spark using the Spark-TS library, a third-party package.<br /> <br /> 在统计学中，预测是推论统计学的一部分。一种特殊的推理方法被称为预测推理，但是这种预测可以在几种推论统计学推理方法中的任何一种中进行。事实上，对统计的一种描述是，它提供了一种将关于某一人口样本的知识转移给整个人口和其他相关人口的手段，这不一定与随着时间的推移所作的预测相同。当信息跨越时间传递，通常是传递到特定的时间点，这个过程就被称为预测。<br /> * 为随机模拟目的而建立完整的统计模型，以产生时间序列的替代版本，反映未来在非特定时间段内可能发生的情况 <br /> * 简单或完整的统计模型，以描述时间序列在最近期间可能产生的结果(预测)。<br /> * 时间序列预测通常使用自动化的统计软件包和编程语言，例如 Julia、 Python、 r、 SAS、 SPSS 等。<br /> * 使用第三方软件包 Spark-TS 库，Apache Spark 可以对大规模数据进行预测。<br /> <br /> ===Classification===<br /> {{main|Statistical classification}}<br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in [[sign language]].<br /> <br /> <br /> Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in sign language.<br /> <br /> = = = 分类 = = 将时间序列模式分配到一个特定的类别，例如根据手语中的一系列动作识别一个单词。<br /> <br /> ===Signal estimation===<br /> {{see also|Signal processing|Estimation theory}}<br /> This approach is based on [[harmonic analysis]] and filtering of signals in the [[frequency domain]] using the [[Fourier transform]], and [[spectral density estimation]], the development of which was significantly accelerated during [[World War II]] by mathematician [[Norbert Wiener]], electrical engineers [[Rudolf E. Kálmán]], [[Dennis Gabor]] and others for filtering signals from noise and predicting signal values at a certain point in time. See [[Kalman filter]], [[Estimation theory]], and [[Digital signal processing]]<br /> <br /> <br /> This approach is based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation, the development of which was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. See Kalman filter, Estimation theory, and Digital signal processing<br /> <br /> = = = 信号估计 = = = 这种方法是基于傅里叶分析信号和滤波的频域使用傅里叶变换和谱密度估计，其发展是显着加速二战期间由数学家诺伯特维纳，电气工程师鲁道夫·卡尔曼，丹尼斯 Gabor 和其他人从噪音信号过滤和预测信号值在一定时间点。参见卡尔曼滤波器，参数估测和数字信号处理<br /> <br /> ===Segmentation===<br /> {{main|Time-series segmentation}}<br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using [[Change detection|change-point detection]], or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> <br /> Splitting a time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in the time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using change-point detection, or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system.<br /> <br /> = = = 分割 = = 将一个时间序列分割成一系列的片段。通常情况下，时间序列可以表示为一系列单独的片段，每个片段都有自己的特征属性。例如，来自电话会议的音频信号可以根据每个人发言的时间分割成相应的部分。在时间序列分割中，目标是识别时间序列中的分段边界点，并刻画每个分段的动态特性。人们可以通过变点检测来解决这个问题，或者将时间序列建模为一个更复杂的系统，如马尔可夫跳跃线性系统。<br /> <br /> ==Models==<br /> <br /> ==Models==<br /> <br /> = = 模型 = = <br /> <br /> Models for time series data can have many forms and represent different [[stochastic processes]]. When modeling variations in the level of a process, three broad classes of practical importance are the ''[[autoregressive]]'' (AR) models, the ''integrated'' (I) models, and the ''[[moving average model|moving average]]'' (MA) models. These three classes depend linearly on previous data points.<ref name="linear time series">{{cite book |author-link=Neil Gershenfeld |last=Gershenfeld |first=N. |year=1999 |title=The Nature of Mathematical Modeling |url=https://archive.org/details/naturemathematic00gers_334 |url-access=limited |location=New York |publisher=Cambridge University Press |pages=[https://archive.org/details/naturemathematic00gers_334/page/n206 205]–208 |isbn=978-0521570954 }}</ref> Combinations of these ideas produce [[autoregressive moving average]] (ARMA) and [[autoregressive integrated moving average]] (ARIMA) models. The [[autoregressive fractionally integrated moving average]] (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for [[vector autoregression]]. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> Models for time series data can have many forms and represent different stochastic processes. When modeling variations in the level of a process, three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. These three classes depend linearly on previous data points. Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models. The autoregressive fractionally integrated moving average (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector autoregression. An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous".<br /> <br /> 时间序列数据的模型可以有多种形式，表示不同的随机过程。在对过程层次的变化进行建模时，三大类实际的重要性是自回归(AR)模型、综合(i)模型和移动平均(MA)模型。这三个类线性地依赖于以前的数据点。这些想法的结合产生了自回归移动平均(ARMA)和 ARIMA模型移动平均(ARIMA)模型。自回归分数积分移动平均(ARFIMA)模型对前三种模型进行了推广。处理矢量值数据的这些类的扩展可以在多元时间序列模型的标题下得到，有时前面的首字母缩略词被扩展，包括一个初始的“ v”代表“矢量”，如在 VAR 代表向量自回归模型。这些模型的另外一组扩展可用于观测到的时间序列是由某种“强迫”的时间序列驱动的(这种时间序列可能对观测到的序列没有因果效应) : 与多变量情况的区别在于强迫序列可能是确定的或者在实验者的控制之下。对于这些模型，首字母缩略词被扩展成最后一个“ x”，表示“外生的”。<br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a [[chaos theory|chaotic]] time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in [[nonlinear autoregressive exogenous model]]s. Further references on nonlinear time series analysis: (Kantz and Schreiber),<ref>{{cite book|last1=Kantz|first1=Holger|last2=Thomas|first2=Schreiber|title=Nonlinear Time Series Analysis|date=2004|publisher=Cambridge University Press|location=London|isbn=978-0521529020}}</ref> and (Abarbanel)<ref>{{cite book|last1=Abarbanel|first1=Henry|title=Analysis of Observed Chaotic Data|date=Nov 25, 1997|publisher=Springer|location=New York|isbn=978-0387983721}}</ref><br /> <br /> Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a chaotic time series. However, more importantly, empirical investigations can indicate the advantage of using predictions derived from non-linear models, over those from linear models, as for example in nonlinear autoregressive exogenous models. Further references on nonlinear time series analysis: (Kantz and Schreiber), and (Abarbanel)<br /> <br /> 一系列数据的水平对以前的数据点的非线性依赖是有趣的，部分是因为产生混沌时间序列的可能性。然而，更重要的是，经验调查可以表明使用来自非线性模型的预测优于来自线性模型的预测，例如在非线性自回归外生模型中。非线性时间序列分析的进一步参考文献: (Kantz 和 Schreiber)和(Abarbanel) <br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time ([[heteroskedasticity]]). These models represent [[autoregressive conditional heteroskedasticity]] (ARCH) and the collection comprises a wide variety of representation ([[GARCH]], TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a [[doubly stochastic model]].<br /> <br /> Among other types of non-linear time series models, there are models to represent the changes of variance over time (heteroskedasticity). These models represent autoregressive conditional heteroskedasticity (ARCH) and the collection comprises a wide variety of representation (GARCH, TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a doubly stochastic model.<br /> <br /> 在其他类型的非线性时间序列模型中，有一些模型可以表示方差随时间的变化(异方差)。这些模型代表了 ARCH模型(ARCH) ，收藏包括各种各样的代表(GARCH，TARCH，EGARCH，FIGARCH，CGARCH 等等)。在这里，变异性的变化与观测系列的最近过去的值有关，或者是预测的。这与局部变化的其他可能表现形式形成对比，在这种情况下，变化可能被模拟为由一个单独的时变过程驱动，如双重随机模型。<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also [[Markov switching multifractal]] (MSMF) techniques for modeling volatility evolution.<br /> <br /> In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose a given time series, attempting to illustrate time dependence at multiple scales. See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution.<br /> <br /> 在最近的无模型分析工作中，基于小波变换的方法(如局部平稳小波和小波分解神经网络)得到了广泛的关注。多尺度(通常称为多分辨率)技术分解给定的时间序列，试图说明在多个尺度上的时间依赖。参见马尔可夫切换多重分形(MSMF)建模波动演化技术。<br /> <br /> A [[Hidden Markov model]] (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest [[dynamic Bayesian network]]. HMM models are widely used in [[speech recognition]], for translating a time series of spoken words into text.<br /> <br /> A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.<br /> <br /> 隐马尔可夫模型模型是一个统计马尔可夫模型，其中被建模的系统被假定为一个具有不可观测(隐藏)状态的马尔可夫过程。隐马尔科姆可以被认为是最简单的动态贝氏网路。隐马尔可夫模型广泛应用于语音识别中，用于将语音序列转换成文本。<br /> <br /> ===Notation===<br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series ''X'' that is indexed by the [[natural number]]s is written<br /> :''X'' = (''X''<sub>1</sub>, ''X''<sub>2</sub>, ...).<br /> <br /> A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written<br /> :X = (X1, X2, ...).<br /> <br /> = = = 表示法 = = 用于时间序列分析的许多不同的表示法。一个用于指定时间序列 x 的通用符号是: x = (X1，X2，...)。<br /> <br /> Another common notation is<br /> :''Y'' = (''Y<sub>t</sub>'': ''t'' ∈ ''T''),<br /> where ''T'' is the [[index set]].<br /> <br /> Another common notation is<br /> :Y = (Yt: t ∈ T),<br /> where T is the index set.<br /> <br /> 另一种常用的表示法是: y = (Yt: t ∈ t) ，其中 t 是索引集。<br /> <br /> ===Conditions===<br /> There are two sets of conditions under which much of the theory is built:<br /> * [[Stationary process]]<br /> * [[Ergodic process]]<br /> <br /> There are two sets of conditions under which much of the theory is built:<br /> * Stationary process<br /> * Ergodic process<br /> <br /> 这个理论的大部分建立在两个条件之下: <br /> * 平稳过程遍历过程<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: [[strict stationarity]] and [[Stationary process#Weaker forms of stationarity|second-order stationarity]]. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> However, ideas of stationarity must be expanded to consider two important ideas: strict stationarity and second-order stationarity. Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified.<br /> <br /> 然而，平稳性的概念必须扩展到考虑两个重要的概念: 严格平稳性和二阶平稳性。模型和应用程序都可以在这些条件中的每一种情况下开发，尽管后一种情况下的模型可能被认为只是部分具体说明。<br /> <br /> In addition, time-series analysis can be applied where the series are [[Cyclostationary process|seasonally stationary]] or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in [[time-frequency analysis]] which makes use of a [[time–frequency representation]] of a time-series or signal.<ref>Boashash, B. (ed.), (2003) ''Time-Frequency Signal Analysis and Processing: A Comprehensive Reference'', Elsevier Science, Oxford, 2003 {{isbn|0-08-044335-4}}</ref><br /> <br /> In addition, time-series analysis can be applied where the series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal.Boashash, B. (ed.), (2003) Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003 <br /> <br /> 此外，时间序列分析可以应用于季节性平稳或非平稳的序列。时频分析利用时间序列或信号的时频表示，可以处理频率分量振幅随时间变化的情况。波阿什，b。我不知道你在说什么。) ，(2003)《时频信号分析与处理: 综合参考》，爱思唯尔科学出版社，牛津，2003<br /> <br /> ===Tools===<br /> Tools for investigating time-series data include:<br /> <br /> Tools for investigating time-series data include:<br /> <br /> = = = 调查时间序列数据的工具包括:<br /> <br /> * Consideration of the [[autocorrelation|autocorrelation function]] and the [[Spectral density|spectral density function]] (also [[cross-correlation function]]s and cross-spectral density functions)<br /> * [[Scaled correlation|Scaled]] cross- and auto-correlation functions to remove contributions of slow components<ref name="Nikolicetal">{{cite journal |last1=Nikolić |first1=D. |last2=Muresan |first2=R. C. |last3=Feng |first3=W. |last4=Singer |first4=W. |year=2012 |title=Scaled correlation analysis: a better way to compute a cross-correlogram |journal=European Journal of Neuroscience |volume=35 |issue=5 |pages=742–762 |doi=10.1111/j.1460-9568.2011.07987.x |pmid=22324876 |s2cid=4694570 |url=https://semanticscholar.org/paper/caa784fc3c22656413143559c402b54d0567f4d1 }}</ref><br /> * Performing a [[Fourier transform]] to investigate the series in the [[frequency domain]]<br /> * Use of a [[digital filter|filter]] to remove unwanted [[noise (physics)|noise]]<br /> * [[Principal component analysis]] (or [[empirical orthogonal function]] analysis)<br /> * [[Singular spectrum analysis]]<br /> * "Structural" models:<br /> ** General [[State Space Model]]s<br /> ** Unobserved Components Models<br /> * [[Machine Learning]]<br /> ** [[Artificial neural network]]s<br /> ** [[Support vector machine]]<br /> ** [[Fuzzy logic]]<br /> ** [[Gaussian process]]<br /> ** [[Genetic Programming]]<br /> ** [[Gene expression programming]]<br /> ** [[Hidden Markov model]]<br /> ** [[Multi expression programming]]<br /> * [[Queueing theory]] analysis<br /> * [[Control chart]]<br /> ** [[Shewhart individuals control chart]]<br /> ** [[CUSUM]] chart<br /> ** [[EWMA chart]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Nonlinear mixed-effects model|Nonlinear mixed-effects modeling]]<br /> * [[Dynamic time warping]]<ref name="Sakoe 1978">{{cite book |last1=Sakoe |first1=Hiroaki |last2=Chiba |first2=Seibi |year=1978 |chapter=Dynamic programming algorithm optimization for spoken word recognition |volume=26 |pages=43–49 |doi=10.1109/TASSP.1978.1163055 |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |s2cid=17900407 |chapter-url=https://semanticscholar.org/paper/18f355d7ef4aa9f82bf5c00f84e46714efa5fd77 }}</ref><br /> * [[Cross-correlation]]<ref>{{cite book |last1=Goutte |first1=Cyril |last2=Toft |first2=Peter |last3=Rostrup |first3=Egill |last4=Nielsen |first4=Finn Å. |last5=Hansen |first5=Lars Kai |year=1999 |chapter=On Clustering fMRI Time Series |volume=9 |issue=3 |pages=298–310 |doi=10.1006/nimg.1998.0391 |pmid=10075900 |journal=NeuroImage |s2cid=14147564 |chapter-url=https://semanticscholar.org/paper/2d5c663fb53d8348bdf3c4df0f881b5db2dcf5e3 }}</ref><br /> * [[Dynamic Bayesian network]]<br /> * [[Time-frequency representation|Time-frequency analysis techniques:]]<br /> ** [[Fast Fourier transform]]<br /> ** [[Continuous wavelet transform]]<br /> ** [[Short-time Fourier transform]]<br /> ** [[Chirplet transform]]<br /> ** [[Fractional Fourier transform]]<br /> * [[Chaos theory|Chaotic analysis]]<br /> ** [[Correlation dimension]]<br /> ** [[Recurrence plot]]s<br /> ** [[Recurrence quantification analysis]]<br /> ** [[Lyapunov exponent]]s<br /> ** [[Entropy encoding]]<br /> <br /> * Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions)<br /> * Scaled cross- and auto-correlation functions to remove contributions of slow components<br /> * Performing a Fourier transform to investigate the series in the frequency domain<br /> * Use of a filter to remove unwanted noise<br /> * Principal component analysis (or empirical orthogonal function analysis)<br /> * Singular spectrum analysis<br /> * "Structural" models:<br /> ** General State Space Models<br /> ** Unobserved Components Models<br /> * Machine Learning<br /> ** Artificial neural networks<br /> ** Support vector machine<br /> ** Fuzzy logic<br /> ** Gaussian process<br /> ** Genetic Programming<br /> ** Gene expression programming<br /> ** Hidden Markov model<br /> ** Multi expression programming<br /> * Queueing theory analysis<br /> * Control chart<br /> ** Shewhart individuals control chart<br /> ** CUSUM chart<br /> ** EWMA chart<br /> * Detrended fluctuation analysis<br /> * Nonlinear mixed-effects modeling<br /> * Dynamic time warping<br /> * Cross-correlation<br /> * Dynamic Bayesian network<br /> * Time-frequency analysis techniques:<br /> ** Fast Fourier transform<br /> ** Continuous wavelet transform<br /> ** Short-time Fourier transform<br /> ** Chirplet transform<br /> ** Fractional Fourier transform<br /> * Chaotic analysis<br /> ** Correlation dimension<br /> ** Recurrence plots<br /> ** Recurrence quantification analysis<br /> ** Lyapunov exponents<br /> ** Entropy encoding<br /> <br /> <br /> * 考虑自相关函数和谱密度函数(也包括互相关函数和互谱密度函数) <br /> * 调整互相关函数和自相关函数以去除慢分量的贡献 <br /> * 在频域中执行一个傅里叶变换来调查这个序列 <br /> * 使用<br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> *CUSUM 图 <br /> * <br /> * EWMA 图 <br /> * 非趋势波动分析 <br /> * 非线性混合效应建模 <br /> * <br /> * 动态时间规整互相关 <br /> * <br /> * 动态贝氏网路 <br /> * 时频分析技术: <br /> * <br /> * 快速傅里叶变换连续小波转换 <br /> * <br /> * 短时距傅里叶变换 <br /> * <br /> * <br /> * <br /> * <br /> * 混沌分析 <br /> * <br /> * <br /> * 复发图 <br /> * <br /> * 递归量化分析 <br /> * <br /> * Lyapunov 指数 <br /> * <br /> * <br /> * <br /> * <br /> <br /> ===Measures===<br /> Time series metrics or [[Features (pattern recognition)|features]] that can be used for time series [[Classification (machine learning)|classification]] or [[regression analysis]]:<ref>{{cite journal |last1=Mormann |first1=Florian |last2=Andrzejak |first2=Ralph G. |last3=Elger |first3=Christian E. |last4=Lehnertz |first4=Klaus |title=Seizure prediction: the long and winding road |journal=[[Brain (journal)|Brain]] |year=2007 |volume=130 |issue=2 |pages=314–333 |doi=10.1093/brain/awl241 |pmid=17008335|doi-access=free }}</ref><br /> <br /> Time series metrics or features that can be used for time series classification or regression analysis:<br /> <br /> = = = = 可用于时间序列分类或回归分析的时间序列度量或特征:<br /> <br /> * '''Univariate linear measures'''<br /> ** [[Moment (mathematics)]]<br /> ** [[Spectral band power]]<br /> ** [[Spectral edge frequency]]<br /> ** Accumulated [[Energy (signal processing)]]<br /> ** Characteristics of the [[autocorrelation]] function<br /> ** [[Hjorth parameters]]<br /> ** [[Fast Fourier transform|FFT]] parameters<br /> ** [[Autoregressive model]] parameters<br /> ** [[Mann–Kendall test]]<br /> * '''Univariate non-linear measures'''<br /> ** Measures based on the [[correlation]] sum<br /> ** [[Correlation dimension]]<br /> ** [[Correlation integral]]<br /> ** [[Correlation density]]<br /> ** [[Correlation entropy]]<br /> ** [[Approximate entropy]]<ref>{{cite web |last1=Land |first1=Bruce |last2=Elias |first2=Damian |title=Measuring the 'Complexity' of a time series |url=http://www.nbb.cornell.edu/neurobio/land/PROJECTS/Complexity/ }}</ref><br /> ** [[Sample entropy]]<br /> ** {{iw2|Fourier entropy||uk|Ентропія Фур'є}}<br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** [[Rényi entropy]]<br /> ** Higher-order methods<br /> ** [[Marginal predictability]]<br /> ** [[Dynamical similarity]] index<br /> ** [[State space]] dissimilarity measures<br /> ** [[Lyapunov exponent]]<br /> ** Permutation methods<br /> ** [[Local flow]]<br /> * '''Other univariate measures'''<br /> ** [[Algorithmic information theory|Algorithmic complexity]]<br /> ** [[Kolmogorov complexity]] estimates<br /> ** [[Hidden Markov Model]] states<br /> ** [[Rough path#Signature|Rough path signature]]<ref>[1] Chevyrev, I., Kormilitzin, A. (2016) "[https://arxiv.org/abs/1603.03788 A Primer on the Signature Method in Machine Learning], arXiv:1603.03788v1"</ref><br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * '''Bivariate linear measures'''<br /> ** Maximum linear [[cross-correlation]]<br /> ** Linear [[Coherence (signal processing)]]<br /> * '''Bivariate non-linear measures'''<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for [[Phase synchronization]]<br /> ** Measures for [[Phase locking]]<br /> * '''Similarity measures''':<ref>{{cite journal |last1=Ropella |first1=G. E. P. |last2=Nag |first2=D. A. |last3=Hunt |first3=C. A. |title=Similarity measures for automated comparison of in silico and in vitro experimental results |journal=Engineering in Medicine and Biology Society |year=2003 |volume=3 |pages=2933–2936 |doi=10.1109/IEMBS.2003.1280532 |isbn=978-0-7803-7789-9 |s2cid=17798157 }}</ref><br /> ** [[Cross-correlation]]<br /> ** [[Dynamic Time Warping]]<ref name="Sakoe 1978"/><br /> ** [[Hidden Markov Models]]<br /> ** [[Edit distance]]<br /> ** [[Total correlation]]<br /> ** [[Newey–West estimator]]<br /> ** [[Prais–Winsten estimation|Prais–Winsten transformation]]<br /> ** Data as Vectors in a Metrizable Space<br /> *** [[Minkowski distance]]<br /> *** [[Mahalanobis distance]]<br /> ** Data as time series with envelopes<br /> *** Global [[standard deviation]]<br /> *** Local [[standard deviation]]<br /> *** Windowed [[standard deviation]]<br /> ** Data interpreted as stochastic series<br /> *** [[Pearson product-moment correlation coefficient]]<br /> *** [[Spearman's rank correlation coefficient]]<br /> ** Data interpreted as a [[probability distribution]] function<br /> *** [[Kolmogorov–Smirnov test]]<br /> *** [[Cramér–von Mises criterion]]<br /> <br /> * Univariate linear measures<br /> ** Moment (mathematics)<br /> ** Spectral band power<br /> ** Spectral edge frequency<br /> ** Accumulated Energy (signal processing)<br /> ** Characteristics of the autocorrelation function<br /> ** Hjorth parameters<br /> ** FFT parameters<br /> ** Autoregressive model parameters<br /> ** Mann–Kendall test<br /> * Univariate non-linear measures<br /> ** Measures based on the correlation sum<br /> ** Correlation dimension<br /> ** Correlation integral<br /> ** Correlation density<br /> ** Correlation entropy<br /> ** Approximate entropy<br /> ** Sample entropy<br /> ** <br /> ** Wavelet entropy<br /> ** Dispersion entropy<br /> ** Fluctuation dispersion entropy<br /> ** Rényi entropy<br /> ** Higher-order methods<br /> ** Marginal predictability<br /> ** Dynamical similarity index<br /> ** State space dissimilarity measures<br /> ** Lyapunov exponent<br /> ** Permutation methods<br /> ** Local flow<br /> * Other univariate measures<br /> ** Algorithmic complexity<br /> ** Kolmogorov complexity estimates<br /> ** Hidden Markov Model states<br /> ** Rough path signature[1] Chevyrev, I., Kormilitzin, A. (2016) "A Primer on the Signature Method in Machine Learning, arXiv:1603.03788v1"<br /> ** Surrogate time series and surrogate correction<br /> ** Loss of recurrence (degree of non-stationarity)<br /> * Bivariate linear measures<br /> ** Maximum linear cross-correlation<br /> ** Linear Coherence (signal processing)<br /> * Bivariate non-linear measures<br /> ** Non-linear interdependence<br /> ** Dynamical Entrainment (physics)<br /> ** Measures for Phase synchronization<br /> ** Measures for Phase locking<br /> * Similarity measures:<br /> ** Cross-correlation<br /> ** Dynamic Time Warping<br /> ** Hidden Markov Models<br /> ** Edit distance<br /> ** Total correlation<br /> ** Newey–West estimator<br /> ** Prais–Winsten transformation<br /> ** Data as Vectors in a Metrizable Space<br /> *** Minkowski distance<br /> *** Mahalanobis distance<br /> ** Data as time series with envelopes<br /> *** Global standard deviation<br /> *** Local standard deviation<br /> *** Windowed standard deviation<br /> ** Data interpreted as stochastic series<br /> *** Pearson product-moment correlation coefficient<br /> *** Spearman's rank correlation coefficient<br /> ** Data interpreted as a probability distribution function<br /> *** Kolmogorov–Smirnov test<br /> *** Cramér–von Mises criterion<br /> <br /> <br /> * 单变量线性测量 <br /> * <br /> * 矩(数学) <br /> * <br /> * 谱带功率 <br /> * <br /> * 谱边缘频率 <br /> * <br /> * 累积能量(信号处理) <br /> * <br /> * 自相关函数特性 <br /> * <br /> * Hjorth 参数 <br /> * <br /> * FFT 参数 <br /> * <br /> * 自回归模型参数 <br /> * <br /> * 相关积分相关密度相关熵近似熵小波熵色散熵涨落色散熵高阶方法边际可预测动力学相似性指数状态空间相异性度量李亚普诺夫指数排列方法<br /> * <br /> * 本地流 <br /> * 其他单变量度量 <br /> * <br /> * 算法复杂度 <br /> * <br /> * 柯氏复杂性估计 <br /> * <br /> * 隐马尔可夫模型状态 <br /> * <br /> * 粗糙路径签名[1] Chevyrev，i. ，Kormilitzin，a。(2016)“ a Primer on the Signature Method in Machine Learning，arXiv: 1603.03788 v1”<br /> * <br /> * 替代时间序列和替代校正 <br /> * <br /> * 递归损失(非平稳度) <br /> * 双变量线性度量 <br /> * <br /> * 最大线性互相关 <br /> * <br /> * 线性相干性(信号处理) <br /> * 双变量非线性度量 <br /> * <br /> * 非线性相互依赖 <br /> * <br /> * <br /> * <br /> * 动态卷吸(物理学) <br /> * <br /> * 相位同步的度量 <br /> * <br /> * 相位锁定的度量 <br /> * <br /> * 相似度量: <br /> * <br /> * 互相关 <br /> * <br /> * <br /> * 动态时间规整 <br /> * <br /> * <br /> * 隐马尔可夫模型 <br /> * <br /> * <br /> * 编辑距离 <br /> * <br /> * 总相关性 <br /> * <br /> * Newey-West 估计 <br /> * <br /> * Prais-Winsten 变换 <br /> * <br /> * 数据作为向量在乌雷松度量化定理 <br /> * <br /> * <br /> * 明氏距离 <br /> * <br /> * 马氏距离 <br /> * <br /> * 数据作为时间序列与信封 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 局部标准差标准差 <br /> * <br /> * <br /> * 窗口标准差 <br /> * <br /> * 数据解释为随机序列 <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * <br /> * 斯皮尔曼的秩相关系数 <br /> * <br /> * 数据解释为概率分布函数 <br /> * <br /> * Kolmogorov-Smirnov 检验 <br /> * <br /> * <br /> * Cramér-von Mises 准则<br /> <br /> ==Visualization==<br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<ref>{{cite web|last1=Tominski|first1=Christian|last2= Aigner|first2=Wolfgang|title=The TimeViz Browser:A Visual Survey of Visualization Techniques for Time-Oriented Data|url=http://survey.timeviz.net/|access-date=1 June 2014}}</ref><br /> <br /> Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on the same layout while Separated Charts presents them on different layouts (but aligned for comparison purpose)<br /> <br /> = = 可视化 = = 时间序列可以用两类图表进行可视化: 重叠图表和分离图表。重叠图表显示同一布局的所有时间序列，而分离图表显示不同的布局(但对齐用于比较)<br /> <br /> ===Overlapping charts===<br /> * [[Braided graphs]]<br /> * Line charts<br /> * Slope graphs<br /> * {{iw2|GapChart||fr}}<br /> <br /> * Braided graphs<br /> * Line charts<br /> * Slope graphs<br /> * <br /> <br /> = = = = 重叠图 = = <br /> * 编织图 <br /> * 线图 <br /> * 斜率图 <br /> * <br /> <br /> ===Separated charts===<br /> * [[Horizon graphs]]<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> * Horizon graphs<br /> * Reduced line chart (small multiples)<br /> * Silhouette graph<br /> * Circular silhouette graph<br /> <br /> = = = = = 分离图表 = = = <br /> * 地平线图 <br /> * 简化线图(小倍数) <br /> * 轮廓线图 <br /> * 圆形轮廓线图<br /> <br /> ==See also==<br /> {{Columns-list|colwidth=30em|<br /> * [[Anomaly time series]]<br /> * [[Chirp]]<br /> * [[Decomposition of time series]]<br /> * [[Detrended fluctuation analysis]]<br /> * [[Digital signal processing]]<br /> * [[Distributed lag]]<br /> * [[Estimation theory]]<br /> * [[Forecasting]]<br /> * [[Frequency spectrum]]<br /> * [[Hurst exponent]]<br /> * [[Least-squares spectral analysis]]<br /> * [[Monte Carlo method]]<br /> * [[Panel analysis]]<br /> * [[Random walk]]<br /> * [[Scaled correlation]]<br /> * [[Seasonal adjustment]]<br /> * [[Sequence analysis]]<br /> * [[Signal processing]]<br /> * [[Time series database]] (TSDB)<br /> * [[Trend estimation]]<br /> * [[Unevenly spaced time series]]<br /> }}<br /> <br /> ==References==<br /> {{Reflist|2}}<br /> <br /> ==Further reading==<br /> * {{Citation<br /> | author-link = George E. P. Box<br /> | last1 = Box | first1 = George<br /> | last2 = Jenkins | first2 = Gwilym<br /> | title = Time Series Analysis: forecasting and control, rev. ed.<br /> | publisher = Holden-Day<br /> | location = Oakland, California<br /> | year = 1976<br /> }}<br /> * [[James Durbin|Durbin J.]], Koopman S.J. (2001), ''Time Series Analysis by State Space Methods'', [[Oxford University Press]].<br /> * {{Citation<br /> | last = Gershenfeld | first = Neil<br /> | year = 2000<br /> | title = The Nature of Mathematical Modeling<br /> | isbn = 978-0-521-57095-4<br /> | publisher = [[Cambridge University Press]]<br /> | oclc = 174825352<br /> }}<br /> * {{Citation<br /> | author-link = James D. Hamilton<br /> | last = Hamilton | first = James<br /> | year = 1994<br /> | title = Time Series Analysis<br /> | isbn = 978-0-691-04289-3<br /> | publisher = [[Princeton University Press]]<br /> }}<br /> * [[Maurice Priestley|Priestley, M. B.]] (1981), ''Spectral Analysis and Time Series'', [[Academic Press]]. {{ISBN|978-0-12-564901-8}}<br /> * {{Citation | last = Shasha | first = D. | title = High Performance Discovery in Time Series | publisher = [[Springer Science+Business Media|Springer]] | year = 2004 | isbn = 978-0-387-00857-8 }}<br /> * Shumway R. H., Stoffer D. S. (2017), ''Time Series Analysis and its Applications: With R Examples (ed. 4)'', Springer, {{ISBN|978-3-319-52451-1}}<br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), ''Time Series Prediction: Forecasting the Future and Understanding the Past''. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), [[Addison-Wesley]].<br /> * [[Norbert Wiener|Wiener, N.]] (1949), ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'', [[MIT Press]].<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), ''Applied Time Series Analysis'', [[CRC Press]].<br /> * {{cite book|last1=Auffarth|first1=Ben|year=2021|title= Machine Learning for Time-Series with Python: Forecast, predict, and detect anomalies with state-of-the-art machine learning methods|publisher=Packt Publishing|edition=1st|isbn=978-1801819626|url=https://www.packtpub.com/product/machine-learning-for-time-series-with-python/9781801819626|access-date=5 November 2021}}<br /> <br /> * <br /> * Durbin J., Koopman S.J. (2001), Time Series Analysis by State Space Methods, Oxford University Press.<br /> * <br /> * <br /> * Priestley, M. B. (1981), Spectral Analysis and Time Series, Academic Press. <br /> * <br /> * Shumway R. H., Stoffer D. S. (2017), Time Series Analysis and its Applications: With R Examples (ed. 4), Springer, <br /> * Weigend A. S., Gershenfeld N. A. (Eds.) (1994), Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis (Santa Fe, May 1992), Addison-Wesley.<br /> * Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press.<br /> * Woodward, W. A., Gray, H. L. & Elliott, A. C. (2012), Applied Time Series Analysis, CRC Press.<br /> * <br /> <br /> = = 进一步阅读 = = <br /> * <br /> * Durbin j，Koopman s.j。(2001) ，《状态空间法时间序列分析》，牛津大学出版社。<br /> * <br /> <br /> * <br /> <br /> * Priestley, M. B.(1981) ，光谱分析与时间序列，学术出版社。<br /> * <br /> * Shumway r. h. ，Stoffer d. s. (2017) ，时间序列分析及其应用: 与 R.示例(ed。4), Springer, <br /> <br /> * Weigend A. S., Gershenfeld N. A.(Eds.)(1994) ，时间序列预测: 预测未来和了解过去。北约比较时间序列分析高级研究讲习班论文集(圣达菲，1992年5月) ，Addison-Wesley。《平稳时间序列的外推、插值和平滑》，麻省理工学院出版社。<br /> * 伍德沃德，w. a. ，格雷，h. l. & 埃利奥特，a. c. (2012) ，应用时间序列分析，CRC 出版社。<br /> *<br /> <br /> ==External links==<br /> {{Commons category}}<br /> *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] — A practical guide to Time series analysis.<br /> <br /> <br /> *Introduction to Time series Analysis (Engineering Statistics Handbook) — A practical guide to Time series analysis.<br /> <br /> = = 外部链接 = = <br /> * 时间序列分析导论(工程统计手册)ー时间序列分析实用指南。<br /> <br /> {{Statistics}}<br /> {{Portal bar|Mathematics}}<br /> {{Authority control}}<br /> <br /> {{DEFAULTSORT:Time Series}}<br /> [[Category:Time series| ]]<br /> [[Category:Statistical data types]]<br /> [[Category:Mathematical and quantitative methods (economics)]]<br /> [[Category:Machine learning]]<br /> <br /> <br /> <br /> Category:Statistical data types<br /> Category:Mathematical and quantitative methods (economics)<br /> Category:Machine learning<br /> <br /> 类别: 统计数据类型类别: 数学和定量方法(经济学)类别: 机器学习<br /> <br /> <noinclude><br /> <br /> <small>This page was moved from [[wikipedia:en:Time series]]. Its edit history can be viewed at [[时间序列分析/edithistory]]</small></noinclude><br /> <br /> [[Category:待整理页面]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E5%B0%8F%E4%B8%96%E7%95%8C%E7%BD%91%E7%BB%9C&diff=33926 小世界网络 2023-01-17T14:39:41Z

<p>TYcl20：</p> <hr /> <div>{{#seo:<br /> |keywords=网络,随机图，小世界，社会网络<br /> |description=小世界模型，集智<br /> }}<br /> <br /> [[File:第一个图.png|200px|缩略图|右|小世界网络的例子中心比其他节点大平均[https://en.wikipedia.org/wiki/Degree_(graph_theory) 度]3.833 平均最短路径长度1.803 [https://en.wikipedia.org/wiki/Clustering_coefficient 聚类系数]0.522]]<br /> [[File:第二个图.png|200px|缩略图|右|随机图平均[https://en.wikipedia.org/wiki/Degree_(graph_theory) 度]2.833 平均最短路径长度2.109 [https://en.wikipedia.org/wiki/Clustering_coefficient 聚类系数]0.167]]<br /> '''小世界网络'''是一种[https://en.wikipedia.org/wiki/Graph_(discrete_mathematics) 数学图]。在这类图中，绝大多数节点互相并不相邻，但任一给定节点的邻居们却很可能彼此是邻居，并且大多数节点都可以从任意其他节点，用较少的步或跳跃访问到。具体来说，小世界网络的定义如下：如果网络中随机选择的两个节点之间的距离<i>L</i>（即访问彼此所需要的步数），与网络中节点数量<i>N</i>的对数成比例增长，（即<ref name="a1">http://www.nature.com/nature/journal/v393/n6684/full/393440a0.html</ref>: <math>L \propto \log N</math>），且网络的[https://en.wikipedia.org/wiki/Clustering_coefficient 集聚系数] Clustering Coefficient不小，那么，这样的网络就是小世界网络。在社交网络中，这种网络属性意味着一些彼此并不相识的人，可以通过一条很短的熟人链条被联系在一起，这也就是[[小世界现象]]。许多经验网络图都展示出了[[小世界现象]]，例如社交网络、互联网的底层架构、Wikipedia的百科类网站及基因网络等。<br /> <br /> 1998年，[[Duncan J. Watts]]和[[Steven Strogatz]]提出，小世界网络是一类[[随机图]]<ref name="a2">Watts, Duncan J.; [https://en.wikipedia.org/wiki/Steven_Strogatz Strogatz, Steven H.] (June 1998). "Collective dynamics of 'small-world' networks". Nature. 393 (6684): 440–442. [https://en.wikipedia.org/wiki/Bibcode Bibcode]:[http://adsabs.harvard.edu/abs/1998Natur.393..440W 1998Natur.393..440W]. [https://en.wikipedia.org/wiki/Digital_object_identifier doi]:[https://doi.org/10.1038/30918 10.1038/30918]. [https://en.wikipedia.org/wiki/PubMed_Identifier PMID] [https://www.ncbi.nlm.nih.gov/pubmed/9623998 9623998]. Papercore Summary http://www.papercore.org/Watts1998</ref>。他们指出，这类网络图可以通过两个独立的结构特征，即[https://en.wikipedia.org/wiki/Clustering_coefficient 集聚系数]和平均节点间距离（也称作平均最短路径长度）来进行识别。根据[[ER随机图模型]]构造的纯随机图，会展现出较小的最短路径长度（通常随着节点数对数值的变化而变化）以及较小的集聚系数。Watts和Strogatz验证了这一点，事实上，现实世界中很多网络的平均最短路径长度都较短，而集聚系数又远高于普通随机图。Watts和Strogatz随后提出了一种新的图模型（即现在的[https://en.wikipedia.org/wiki/Watts_and_Strogatz_model Watts-Strogatz模型]），该模型具备两个特征：(1)平均最短路径长度较小，(2)集聚系数较大。1999年，Barthelemy和Amaral最先描述出了Watts-Strogatz模型中“大世界”（诸如栅格网络）与小世界的交叉点性质<ref name="a3">#Barthelemy, M.; Amaral, LAN (1999). "Small-world networks: Evidence for a crossover picture". Phys. Rev. Lett. 82 (15): 3180–3183. [https://en.wikipedia.org/wiki/ArXiv arXiv]:[https://arxiv.org/abs/cond-mat/9903108 cond-mat/9903108]. Bibcode:1999PhRvL..82.3180B. doi:10.1103/PhysRevLett.82.3180.</ref>。在此之后，学界又涌现出了大量的相关研究，其中不乏一些较为精确的度量结果 (Barrat and Weigt, 1999; Dorogovtsev and [https://en.wikipedia.org/wiki/Jos%C3%A9_Fernando_Ferreira_Mendes Mendes]; Barmpoutis and Murray, 2010)。 Braunstein发现<ref name="a4">#Braunstein, Lidia A.; Buldyrev, Sergey V.; Cohen, Reuven; Havlin, Shlomo; Stanley, H. Eugene (2003). "Optimal Paths in Disordered Complex Networks". Physical Review Letters. 91 (16). arXiv:cond-mat/0305051 Freely accessible. Bibcode:2003PhRvL..91p8701B. doi:10.1103/PhysRevLett.91.168701. ISSN 0031-9007.</ref>，对于权值分布非常广的加权ER网络，最佳路径长度会显著增长，其增长速度为<math>N^{\frac{1}{3}}</math>.<br /> <br /> ==小世界网络的性质==<br /> <br /> <br /> 小世界网络中往往会包含''' 团 cliques''' 以及'''临近团 near-cliques''' ——此处的“团”，指的是内部几乎任意两个节点之间都存在连接的子网络。这遵循[https://en.wikipedia.org/wiki/Clustering_coefficient 高集聚系数]的定义属性。其次，大多数节点对之间，都至少存在一条短路径。这遵循平均最短路径较小的定义属性。许多其他属性，通常也会与小世界网络有所关联。通常情况下，网络中会存在很多的'''中心 hub''' ——它们是具有很高连接数的节点（即高度节点）。这些中心扮演了公共连接的角色，缩短了其他边之间的短路径长度。通过对比，航空航班的小世界网络，都体现出了较短的平均路径长度（例如，在任意两个城市之间飞行，你通常可能只需要乘坐三程或更少的航班数），因为很多航线都可以通过枢纽城市进行中转。这一属性的分析，通常要考虑网络中，具有相同入度的节点的比例（网络的度的分布）。网络具有较多中心，意味着度值较大的节点占比会更高，因此，在这种网络的度分布中，高度值分布更高，即俗称的[https://en.wikipedia.org/wiki/Fat-tailed_distribution 厚尾分布] fat-tailed distribution 。具有不同拓扑结构的图，只要满足上述两个定义，就可以被定义为'''小世界网络'''。<br /> <br /> 网络的小世界性被量化为一个系数<math>\sigma </math>，可以通过比较给定网络与具备相同度分布的等价网络的集聚系数与路径长度，计算得出<ref name="a5">#The brainstem reticular formation is a small-world, not scale-free, network M. D. Humphries, K. Gurney and T. J. Prescott, Proc. Roy. Soc. B 2006 273, 503–511, doi:10.1098/rspb.2005.3354</ref><ref name="a6">#Humphries and Gurney (2008). "[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2323569 Network 'Small-World-Ness': A Quantitative Method for Determining Canonical Network Equivalence]". PLOS ONE. 3 (4): e0002051. doi:10.1371/journal.pone.0002051. PMC 2323569 Freely accessible. PMID 18446219.</ref>。<br /> <br /> :<math>\sigma = \cfrac { \frac {C} {C_r} } { \frac {L} {L_r} } </math><br /> <br /> 如果<math> \sigma > {1}</math>( <math> C \gg C_r </math>，且<math>L \approx L_r</math>), 网络即为小世界网络<br /> <br /> 另一个量化网络小世界性的方法，是利用小世界网络的原始定义，比较给定网络与等价随机网格网络的集聚系数及路径长度<ref name="a7">#The ubiquity of small-world networks Q.K. Telesford, K.E. Joyce, S. Hayasaka, J.H. Burdette, P.J. Laurienti, Brain Connect. 2011;1(5):367–75, doi:10.1089/brain.2011.0038</ref>。小世界所用的度量（<math> \omega</math>）定义如下<ref name="a8">#Telesford, Joyce, Hayasaka, Burdette, and Laurienti (2011). "[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3604768 The Ubiquity of Small-World Networks]". Brain Connectivity. 1 (0038): 367–75. doi:10.1089/brain.2011.0038. PMC 3604768 Freely accessible. PMID 22432451.</ref>：<br /> <br /> :<math> \omega = \frac{L_r}{L}-\frac{C}{C_l} </math><br /> <br /> 其中，对于所选受测网络而言，<i>L</i>是特征路径长度，<i>C</i>是集聚系数。<math>C_l</math>是等价栅格网络的集聚系数，而<math>L_r</math>则是等价随机网络的的特征路径长度。<br /> <br /> R. Cohen和[https://en.wikipedia.org/wiki/Shlomo_Havlin Havlin]分析出<ref name="a9">#R. Cohen, S. Havlin, and D. ben-Avraham (2002). "[http://havlin.biu.ac.il/Publications.php?keyword=Structural+properties+of+scale+free+networks&year=*&match=all Structural properties of scale free networks]". Handbook of graphs and networks. Wiley-VCH, 2002 (Chap. 4).</ref><ref name="a10">#R. Cohen, S. Havlin (2003). "[http://havlin.biu.ac.il/Publications.php?keyword=Scale-free+networks+are+ultrasmall++&year=*&match=all Scale-free networks are ultrasmall]". Phys. Rev. Lett. 90 (5): 058701. arXiv:cond-mat/0205476. Bibcode:2003PhRvL..90e8701C. doi:10.1103/PhysRevLett.90.058701. PMID 12633404.</ref>，[[无标度网络]]是超小世界。在这种情况下，由于中心的存在，最短路径会变得非常小，并且满足如下关系：<br /> <br /> :<math> L \propto \log{\log N}</math><br /> <br /> 结果表明，在存在[https://en.wikipedia.org/wiki/White_noise 白噪音]的小世界网络中，会出现随机同步，这意味着，白噪音有助于系统针对中等噪声强度进行更好地同步，而非减少噪音<ref name="a11">#Reihaneh Kouhi Esfahani, Farhad Shahbazi, Keivan Aghababaei Samani (2012). "[https://journals.aps.org/pre/abstract/10.1103/PhysRevE.86.036204 Noise-induced synchronization in small-world networks of phase oscillators]". Physical Review E. American Physical Society (3).</ref><ref name="a12">#Rodrigues, Francisco A and Peron, Thomas K DM and Ji, Peng and Kurths, J{\"u}rgen} (2016). "[https://www.sciencedirect.com/science/article/pii/S0370157315004408 The Kuramoto model in complex networks]". Physics Reports. Elsevier.</ref>。这种现象，与白噪音在[[随机图]]或[[无标度网络]]中的效果形成了鲜明的对比，即应用噪声会降低这些网络中的同步幅度，使同步的效率提高。<br /> <br /> ==小世界网络例子==<br /> <br /> <br /> 在现实世界的很多现象中，都能够看到小世界属性，这包括网络中的导航菜单、食物网、电网、代谢处理网络 metabolite processing networks 、[https://en.wikipedia.org/wiki/Biological_neural_network 脑神经网络]、选民网络、电话呼叫图、社交影响网络等等。文化网络<ref name="a13">#" 'n [http://www.litnet.co.za/n-kwantifisering-van-kleinwereldsheid-in-afrikaanse-kultuurnetwerke-in-vergelyking-met-ander-komplekse-netwerke/ Kwantifisering van kleinwêreldsheid in Afrikaanse kultuurnetwerke in vergelyking met ander komplekse netwerke | LitNet]". LitNet. 2015-11-05. Retrieved 2017-02-27.</ref>与单词共现网络<ref name="a14">#"[http://www.litnet.co.za/die-statistiese-eienskappe-van-geskrewe-afrikaans-n-komplekse-netwerk/ Die statistiese eienskappe van geskrewe Afrikaans as 'n komplekse netwerk | LitNet]". LitNet. 2017-02-09. Retrieved 2017-02-27.</ref>也被证明是小世界网络。<br /> <br /> 相连的蛋白质网络同样具有小世界性质，例如遵从幂律的度分布。<ref name="a15">#Bork, P.; Jensen, LJ; von Mering, C.; Ramani, A.; Lee, I.; Marcotte, EM. (2004). "[http://marcottelab.org/paper-pdfs/cosb-review.pdf Protein interaction networks from yeast to human]" (PDF). Current Opinion in Structural Biology. 14 (3): 292–299. doi:10.1016/j.sbi.2004.05.003. PMID 15193308.</ref>类似地还有[https://en.wikipedia.org/wiki/Transcriptional_regulation 转录网络]，其节点为[https://en.wikipedia.org/wiki/Gene 基因]，如果某一个基因对另一个基因有上调或下调的遗传影响，且这些基因彼此相连，这一网络就具有小世界网络的性质。<ref name="a16">#Van Noort, V; Snel, B; Huynen, MA. (Mar 2004). "[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1299002 The yeast coexpression network has a small-world, scale-free architecture and can be explained by a simple model]". EMBO Rep. 5 (3): 280–4. doi:10.1038/sj.embor.7400090. PMC 1299002 Freely accessible. PMID 14968131.</ref><br /> <br /> ==非小世界网络例子==<br /> <br /> <br /> 另一个例子就是人与人之间的“[https://en.wikipedia.org/wiki/Six_degrees_of_separation 六度分离]”理论。该理论的适用条件是假设涉及到的人都同时活着，或者在短期内处于同一组织之中。[https://en.wikipedia.org/wiki/Albert_Einstein 阿尔伯特·爱因斯坦]与[https://en.wikipedia.org/wiki/Alexander_the_Great 亚历山大大帝]之间的分离度，几乎肯定是大于30的<ref name="a17">#Einstein and Alexander the Great lived 2202 years apart. Assuming an age difference of 70 years between any two connected people in the chain that connects the two, this would necessitate at least 32 connections between Einstein and Alexander the Great.</ref>，而且这个世界并不具备小世界属性。一个同样不具备小世界性质的网络还有“曾去同一家学校上学”的网络：如果两个人加入某一所大学的时间差了10年，他们不太可能在学生团体中有共同的熟人。<br /> <br /> 类似的，消息传播过程中必须要通过的中继站点的数量并不总是很少的。回溯到邮件还需要手工投递或骑马寄送的时期，一封信件从它的起点到终点所需要转手的次数，会比现在大上很多。可视电报（约存在于1800-1850年）时代，消息易手的次数，要由两个站点之间是否是在视线连接范围内决定。<br /> <br /> 如果没有检验隐含假设，可能会对图“望图生义”，偏向于寻找小世界网络（一个例子就是发表性偏倚导致的[https://en.wikipedia.org/wiki/File_drawer_problem#File_drawer_effect 文件抽屉问题] file drawer ）。<br /> <br /> ==网络鲁棒性==<br /> <br /> <br /> [https://en.wikipedia.org/wiki/Albert-L%C3%A1szl%C3%B3_Barab%C3%A1si Barabási]等研究人员提出假设，认为小世界网络在生物系统中的普遍存在，可能反映了这种结构的进化优势。一种可能性是，小世界网络相比其他网络架构，对扰动的鲁棒性更强。如果这种假设成立，小世界网络将为受到突变或病毒感染损害的生物系统提供优势。<br /> <br /> 在一个具备遵循[[幂律分布]]现象的度分布的小世界网络中，随机删除节点，极少能导致平均最短路径长度显著增加（或[https://en.wikipedia.org/wiki/Clustering_coefficient 集聚系数]的显著降低）。这是因为，节点之间的最短路径通过[https://en.wikipedia.org/wiki/Hub_(network_science) 中心]点流动，而且，如果一个外围节点被删除，不太可能干扰其他外围节点之间的通路。由于小世界网络中，外围节点的比例要远高于中心的比例，因此，删除重要节点的概率非常低。例如，如果爱达荷州太阳谷的小型机场被关闭，不会增加在美国旅行的其他乘客到达各自目的地所需的平均航次。但是，如果随机删除的节点是中心枢纽，那么平均路径长度就会急剧增加。每年都可以看到，当芝加哥奥黑尔机场等北部枢纽因大雪关闭时，经常会出现这种状况；许多乘客不得不搭乘更多航班，以达到目的地。<br /> <br /> 相反，在随机网络中，所有节点具有数量大致相同的连接，随机删除节点可能会略微增加平均最短距离，但删除任意节点都会带来这样的影响。从这个意义上来讲，随机网络容易受到随机扰动的影响，而小世界网络则具备鲁棒性。但是，小世界网络容易受到针对中心的攻击，而目标攻击无法对随机网络造成灾难性故障。<br /> <br /> 病毒已经进化到可以干扰中枢蛋白的活动，诸如[https://en.wikipedia.org/wiki/P53 p53]，并因此产生有利于病毒复制的细胞行为的巨大变化。渗流理论是分析网络鲁棒性的一个有效方法。<br /> <br /> ==构建小世界网络==<br /> <br /> <br /> 构建小世界网络的主要机制是'''[https://en.wikipedia.org/wiki/Watts_and_Strogatz_Model Watts-Strogatz机制]'''。<br /> <br /> 小世界网络也可引入延时<ref name="a18">#X. S. Yang, Fractals in small-world networks with time-delay, Chaos, Solitons & Fractals, vol. 13, 215–219 (2002)<br /> </ref>，这不仅会产生分形，而且在特定条件下，还会形成混沌<ref name="a19">#X. S. Yang, Chaos in small-world networks, Phys. Rev. E 63, 046206 (2001)<br /> </ref>，或者在动态网络中转变为混沌<ref name="a20">#W. Yuan, X. S. Luo, P. Jiang, B. Wang, J. Fang, Transition to chaos in small-world dynamical network<br /> </ref>。<br /> <br /> 构造[https://en.wikipedia.org/wiki/Degree_diameter 度直径图] Degree–diameter graph 的方法是：网络中每个顶点的邻居数量是有界的，而网络中从任意给定顶点到其他顶点（网络直径）是最小的。构建这样的小世界网络，其实是为寻找临近[https://en.wikipedia.org/wiki/Moore_graph 摩尔边界]的图的秩，而做出的一部分努力。<br /> <br /> Barmpoutis等人给出的从零开始构建小世界网络的另外一种方法<ref name="a21">#[https://en.wikipedia.org/wiki/D.Barmpoutis_and_R.M._Murray D.Barmpoutis and R.M. Murray] (2010). "Networks with the Smallest Average Distance and the Largest Average Clustering". arXiv:1007.4031 Freely accessible [q-bio.MN].</ref>，构建了一种平均距离极小且平均集聚度极高的网络。他们提到了一种复杂度恒定的快速算法，以及不同生成图鲁棒性的度量。根据每个网络的应用，可以从一个这样的“超小世界”网络开始，然后重新连接一些边，或者使用几个这样的小网络作为子图，构筑一个更大的图。<br /> <br /> 通过[https://en.wikipedia.org/wiki/Dual-phase_evolution 双相演化] dual-phase evolution 过程，小世界属性可以在社交网络和其他现实世界系统中自然产生。在顶点之间的连接增长受到时间或空间的制约时，小世界网络尤其常见。该机制通常涉及相位之间的周期性变换，其中，在“全局”阶段——连接建立，而在“本地”阶段——连接被移除。<br /> <br /> 参考：[https://en.wikipedia.org/wiki/Diffusion-limited_aggregation 扩散限制凝聚]，[https://en.wikipedia.org/wiki/Pattern_formation 模式构成]。<br /> <br /> ==构建小世界网络代码实现==<br /> <br /> === 使用networkx生成小世界网络 ===<br /> <syntaxhighlight lang="python"><br /> <br /> import networkx as nx<br /> import matplotlib.pyplot as plt<br /> <br /> # WS network<br /> # 生成20个节点的小世界网络<br /> # 每个节点有四个邻居<br /> # 每条连边以0.3的概率随机重置链接<br /> WS = nx.random_graphs.watts_strogatz_graph(20, 4, 0.3)<br /> pos = nx.circular_layout(WS)<br /> nx.draw(WS, pos, with_labels = False, node_size = 30)<br /> plt.show()<br /> <br /> </syntaxhighlight><br /> <br /> 此时得到的图片是下图所示:<br /><br /> [[File:第三个图.png | 400px]]<br /> <br /> === 使用原生方法x生成小世界网络 ===<br /> <syntaxhighlight lang="python"><br /> G = nx.Graph()<br /> node_num = 20<br /> neighbour_num = 4<br /> probility = 0.3<br /> # 节点与邻居相连<br /> for i in range(node_num):<br /> from_node = i<br /> for j in range(neighbour_num):<br /> to_node = (i+j) % node_num - neighbour_num / 2<br /> if to_node >= 0:<br /> to_node += 1<br /> G.add_edge(from_node,to_node)<br /> # 连边随机重连<br /> edges = copy.deepcopy(G.edges())<br /> for edge in edges:<br /> if random.random() < probility:<br /> G.remove_edge(edge[0],edge[1])<br /> ran_edge = np.random.randint(node_num,size=2).tolist()<br /> G.add_edge(ran_edge[0],ran_edge[1])<br /> # 绘图<br /> pos = nx.circular_layout(G)<br /> nx.draw(G, pos, with_labels = False, node_size = 30)<br /> plt.show()<br /> </syntaxhighlight><br /> <br /> 此时得到的图片如下图所示：<br /> <br /><br /> [[File:第四个图.png |400px]]<br /> <br /> ==应用==<br /> <br /> <br /> ===社会学应用===<br /> <br /> 小世界网络对[https://en.wikipedia.org/wiki/Social_movement 社会运动群体]的优势在于，它们由于采用了高度互联的节点的过滤设备，因而对变化具有一定的抗性，以及它有效地实现了，在中继信息的同时，保持了连接网络所需的最少链路数”。<ref name="a22">#Shirky, Clay. 2008. [https://en.wikipedia.org/wiki/Here_Comes_Everybody Here Comes Everybody]</ref><br /> <br /> [https://en.wikipedia.org/wiki/William_Finnegan William Finnegan]在社会学论证提出，小世界网络可直接适用于[https://en.wikipedia.org/wiki/Affinity_group 亲和团体] Affinity Group 理论。亲和团体指的是旨在实现某个较大目标或功能的小型半独立社会运动团体。虽然在节点级别上并没有严格的隶属架构，但作为连接节点的少数高连接性成员，能够通过网络连接组织内的不同群体。这种小世界网络已被证明是一种极其有效的抗议警察行动的组织策略。<ref name="a23">#Finnegan, William "Affinity Groups and the Movement Against Corporate Globalization"</ref>[https://en.wikipedia.org/wiki/Clay_Shirky Clay Shirky]认为，通过小世界网络创造的社交网络越大，高连接性结点在网络内的价值就越高。<ref name="a22"></ref>同理可适用于亲和团体模型，即每个团体内只有少数人与外部团体相联系，从而极大提高了灵活性和适应性。这方面的一个实践案例是William Finnegan在概括1999年西雅图世贸组织抗议活动时，所提到的亲和团体中的小世界网络。<br /> <br /> ===地球科学应用===<br /> <br /> 许多研究地质学和地球物理学的网络，已被证明具有小世界网络的特征。在裂缝系统和多空物质中被定义的网络，已经显示出了这些特征。<ref name="a24">#X. S. Yang, Small-world networks in geophysics, Geophys. Res. Lett., 28(13), 2549–2552 (2001)<br /> </ref>南加州地区的地震网络或许就是一个小世界网络。<ref name="a25">#A. Jimenez, K. F. Tiampo, and A. M. Posadas, Small-world in a seismic network: the California case, Nonlin. Processes Geophys., 15, 389–395 (2008)</ref>上述提及的例子所发生的空间尺度大相径庭，也证明了在地球科学中，这一现象不受空间尺度大小所影响，具备[https://en.wikipedia.org/wiki/Scale_invariance 尺度不变性] scale invariance 。气候网络或许也可被视作小世界网络，其中的联系具备长度不一的尺度。<ref name="a26">#Gozolchiani, A.; Havlin, S.; Yamasaki, K. (2011). "Emergence of El Niño as an Autonomous Component in the Climate Network". Physical Review Letters. 107 (14): 148501. arXiv:1010.2605 Freely accessible. Bibcode:2011PhRvL.107n8501G. doi:10.1103/PhysRevLett.107.148501. ISSN 0031-9007. PMID 22107243.<br /> </ref><br /> <br /> ===计算应用===<br /> <br /> 小世界网络已被用于估算存储于大型数据库中信息的可用性。这种度量方法被称为“小世界数据变换法”<ref name="a27"># http://mike2.openmethodology.org/wiki/Small_Worlds_Data_Transformation_Measure</ref><ref name="a28">#Hillard, Robert (2010). Information-Driven Business. Wiley. ISBN 978-0-470-62577-4.</ref>数据库链接与小世界网络对齐度越高，用户越有可能在将来提取到信息。这种可用性通常以牺牲存储在同等空间中的信息量为代价来取得。<br /> <br /> [https://en.wikipedia.org/wiki/Freenet Freenet]和[https://en.wikipedia.org/wiki/Bitcoin_Cash 比特币]点对点网络已经被证明在模拟中构筑了小世界网络<ref name="a29">#Sandberg, Oskar. "[https://freenetproject.org/papers/lic.pdf Searching in a Small World]" (PDF).<br /> </ref>，使得信息的存储和提取，能够随着网络扩展，而有效扩张。<br /> <br /> ===大脑中的小世界网络===<br /> <br /> 大脑中连接<ref name="a30">#Sporns, Olaf; Chialvo DR; Kaiser M; Hilgetag CC (2004). "Organization, development and function of complex brain networks". Trends Cogn Sci. 8 (9): 418–425. doi:10.1016/j.tics.2004.07.008. PMID 15350243.<br /> </ref>与皮层神经元的同步网络<ref name="a31">#Yu, Shan; D. Huang; W. Singer; D. Nikolić (2008). "[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2583154 A Small World of Neuronal Synchrony]". Cerebral Cortex. 18 (12): 2891–2901. doi:10.1093/cercor/bhn047. PMC 2583154 Freely accessible. PMID 18400792.</ref>都体现出了小世界拓扑结构。<br /> <br /> 小世界神经元网络可以呈现出短期记忆。Solla等人提出的计算机模型具有两个稳定状态<ref name="a32">#Cohen, Philip. [https://www.newscientist.com/article.ns?id=dn5012 Small world networks key to memory]. New Scientist. 26 May 2004.</ref><ref name="a33">#Sara Solla's [http://online.itp.ucsb.edu/online/brain04/solla/ Lecture & Slides: Self-Sustained Activity in a Small-World Network of Excitable Neurons]</ref>——一种被认为在记忆存储中十分重要的特性（被称为[https://en.wikipedia.org/wiki/Bistability 双稳态]）。激活脉冲在神经元之间产生自我维持的通信活动循环。第二波脉冲则终止这一活动。脉冲让这一系统在稳定状态间切换：流动（记录“记忆”）以及停滞（保留记忆）。小世界神经元网络也被用于建模，了解[https://en.wikipedia.org/wiki/Seizures 病情发作]的原理。<ref name="a34">#Ponten, S.C.; Bartolomei, F.; Stam, C.J. (April 2007). "Small-world networks and epilepsy: Graph theoretical analysis of intracerebrally recorded mesial temporal lobe seizures". Clinical Neurophysiology. 118 (4): 918–927. doi:10.1016/j.clinph.2006.12.002.</ref><br /> <br /> 在更一般的层次上，大脑中的许多大规模神经网络，例如视觉系统和脑干，都体现出了小世界特性。<ref name="a5"></ref><br /> <br /> ==小世界的连接长度分布==<br /> <br /> WS模型包含了一个长域连接的均匀分布。当连接长度的分布遵循“幂次现象”分布时，两个结点之间平均距离的变化，取决于分布的幂次。<ref name="a35">#D. Li, K. Kosmidis, A. Bunde, S. Havlin (2011). "[http://havlin.biu.ac.il/Publications.php?keyword=Dimension+of+spatially+embedded+networks&year=*&match=all Dimension of spatially embedded networks]". Nature Physics. 7: 481–484. Bibcode:2011NatPh...7..481D. doi:10.1038/nphys1932.</ref><br /> <br /> ==参见==<br /> *[[BA模型]]<br /> *[https://en.wikipedia.org/wiki/Climate_network 气候网络]<br /> *[https://en.wikipedia.org/wiki/Dual-phase_evolution 双相演化 Dual-phase evolution]<br /> *[https://en.wikipedia.org/wiki/Dunbar%27s_number Dunbar数]<br /> *[https://en.wikipedia.org/wiki/Erd%C5%91s_number Erdős数]<br /> *[[ER随机图模型]]<br /> *[[渗透理论 Percolation theory]]<br /> *[[无标度网络]]<br /> *[https://en.wikipedia.org/wiki/Six_degrees_of_Kevin_Bacon Kevin Bacon的六度理论]<br /> *[https://en.wikipedia.org/wiki/Small_world_experiment 小世界实验]<br /> *[https://en.wikipedia.org/wiki/Social_network 社交网络]<br /> *[https://en.wikipedia.org/wiki/Watts_and_Strogatz_model Watts Strogatz模型]<br /> <br /> ==参考==<br /> <references/><br /> <br /> ===书籍===<br /> <br /> *Buchanan, Mark (2003). Nexus: Small Worlds and the Groundbreaking Theory of Networks. Norton, W. W. & Company, Inc. ISBN 0-393-32442-7.<br /> *Dorogovtsev, S.N. & Mendes, J.F.F. (2003). Evolution of Networks: from biological networks to the Internet and WWW. Oxford University Press. ISBN 0-19-851590-1.<br /> *Watts, D. J. (1999). Small Worlds: The Dynamics of Networks Between Order and Randomness. Princeton University Press. ISBN 0-691-00541-9.<br /> *Fowler, JH. (2005) "Turnout in a Small World," in Alan Zuckerman, ed., Social Logic of Politics, Temple University Press, 269–287<br /> *Reuven Cohen and Shlomo Havlin (2010). Complex Networks: Structure, Robustness and Function. Cambridge University Press.<br /> <br /> ===期刊===<br /> <br /> *Albert, R.; Barabási A.L. (2002). "Statistical mechanics of complex networks". Rev. Mod. Phys. 74: 47–97. arXiv:cond-mat/0106096 Freely accessible. Bibcode:2002RvMP...74...47A. doi:10.1103/RevModPhys.74.47.<br /> *Albert, R.; Barabási A.L. (1999). "Emergence of scaling in random networks". Science. 286 (5439): 509–12. arXiv:cond-mat/9910332 Freely accessible. Bibcode:1999Sci...286..509B. doi:10.1126/science.286.5439.509. PMID 10521342.<br /> *Barthelemy, M.; Amaral, LAN. (1999). "Small-world networks: Evidence for a crossover picture". Phys. Rev. Lett. 82 (15): 3180–3183. arXiv:cond-mat/9903108 Freely accessible. Bibcode:1999PhRvL..82.3180B. doi:10.1103/PhysRevLett.82.3180.<br /> *Dorogovtsev, S.N.; Mendes, J.F.F. (2000). "Exactly solvable analogy of small-world networks". Europhys. Lett. 50: 1–7. arXiv:cond-mat/9907445 Freely accessible. Bibcode:2000EL.....50....1D. doi:10.1209/epl/i2000-00227-1.<br /> *Milgram, Stanley (1967). "The Small World Problem". Psychology Today. 1 (1): 60–67.<br /> *Newman, Mark (2003). "The Structure and Function of Complex Networks". SIAM Review. 45 (2): 167–256. arXiv:cond-mat/0303516 Freely accessible. Bibcode:2003SIAMR..45..167N. doi:10.1137/S003614450342480. pdf<br /> *Ravid, D.; Rafaeli, S. (2004). "Asynchronous discussion groups as Small World and Scale Free Networks". First Monday. 9 (9). doi:10.5210/fm.v9i9.1170. [1]<br /> *R. Parshani, S.V. Buldyrev, S. Havlin (2011). "Critical effect of dependency groups on the function of networks". PNAS. 108: 1007–1010. arXiv:1010.4498 Freely accessible. *Bibcode:2011PNAS..108.1007P. doi:10.1073/pnas.1008404108. PMC 3024657 Freely accessible. PMID 21191103.<br /> *S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, S. Havlin (2010). "Catastrophic cascade of failures in interdependent networks". Nature. 464 (7291): 1025–8. arXiv:0907.1182 Freely accessible. Bibcode:2010Natur.464.1025B. doi:10.1038/nature08932. PMID 20393559.<br /> <br /> ==相关链接==<br /> <br /> *[http://demonstrations.wolfram.com/DynamicProximityNetworks 动态临近网络] Seth J. Chandler, [https://en.wikipedia.org/wiki/The_Wolfram_Demonstrations_Project Wolfram展示项目]<br /> *[http://www.scholarpedia.org/article/Small-world_network 小世界网络]词条, Scholarpedia (Mason A. Porter)<br /> <br /> == 编者推荐 ==<br /> <br /> === 集智文章推荐 ===<br /> <br /> [[File:第五张图.png|190px|thumb|right|什么是小世界模型]]<br /> ====[https://swarma.org/?p=19627 什么是小世界网络模型]====<br /> :我们需要了解小世界网络是一种数学图。在这种图中，绝大多数节点之间并不相邻，但任一给定节点的邻居们却很可能彼此相邻，并且大多数任意节点，都可以用较少的步或跳跃访问到其他节点。在社交网络中，这种网络属性意味着一些彼此并不相识的人，可以通过一条很短的熟人链条被联系在一起，这也就是小世界现象。<br /> <br /> <br /> [[File:第六张图.png|190px|thumb|right|论文题目]]<br /> ====[https://swarma.org/?p=18837 引用量超过4万的经典论文：小世界网络的集体动力学]====<br /> :1998年，一篇名为“小世界网络的集体动力学” Collective dynamics of ‘small-world’ networks 的文章发表于 Nature，首次提出“小世界网络”的数学模型，并引起了来自社会科学、信息科学和自然科学等领域对这一模型的关注和应用。目前，该论文已经有超过 42000 次的引用量。本文是对这篇经典论文的简要介绍。<br /> <br /> <br /> === 集智课程推荐 ===<br /> ====[https://campus.swarma.org/course/1347 Networks]====<br /> :本课程中，介绍网络的相关的概念与小世界网络、无标度网络。<br /> <br /> <br /> ====[https://campus.swarma.org/course/1161 复杂网络的基本模型]====<br /> :本课程中，将详细介绍复杂网络的四个基本模型：规则网、随机图、小世界网络、Scale-Free 网络。<br /> <br /> <br /> <br /> ----<br /> 本中文词条由[[用户:Sherimon|Sherimon]]、[[用户:Jake|Jake]]、[[用户:Wanting|Wanting]]编译，[[用户:许许|许许]]编辑，欢迎在讨论页面留言。<br /> <br /> <br /> '''本词条内容源自公开资料，遵守 CC3.0协议。'''<br /> <br /> [[Category:复杂系统]]<br /> [[Category:社会网络]]<br /> [[Category:随机图]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E8%87%AA%E7%BB%84%E7%BB%87&diff=33925 自组织 2023-01-17T12:32:56Z

<p>TYcl20：</p> <hr /> <div>{{#seo:<br /> |keywords=自组织 Self-organization <br /> |description=也被称为自发秩序，是指一种起源于初始无序系统的部分元素之间的局部相互作用、所产生出某种形式的整体秩序的过程。 }}<br /> <br /> [[File:Nb3O7(OH)_self-organization2.jpg|400px|thumb|right|在200°C 的水热处理期间，微米级,<math>Nb_3O_7(OH)</math>立方体中的自组织。最初，无定形立方体逐渐转变为晶体纳米线的有序3D网格，如图模型所示。<ref>{{Cite journal | doi= 10.1039/C4TA02202E| title= Template-free synthesis of novel, highly-ordered 3D hierarchical Nb<sub>3</sub>O<sub>7</sub>(OH) superstructures with semiconductive and photoactive properties| journal= Journal of Materials Chemistry A| volume= 2| issue= 30| page= 12005| year= 2014| last1= Betzler | first1= S. B. | last2= Wisnet | first2= A. | last3= Breitbach | first3= B. | last4= Mitterbauer | first4= C. | last5= Weickert | first5= J. | last6= Schmidt-Mende | first6= L. | last7= Scheu | first7= C. |doi-access= free| url= https://kops.uni-konstanz.de/bitstream/123456789/28968/1/Betzler_289681.pdf}}</ref>]]<br /> '''自组织 Self-organization'''，在社会科学中也被称为[[自发秩序]]''Spontaneous order'' ，是指通过起源于初始无序系统的部分元素之间的局部发生相互作用，使某种形式的整体秩序形成的过程。当有足够的能量可用时，该过程可以是自发的，不需要任何外部主体进行控制。它是由看似随机的扰动触发的，并由正反馈放大，最终形成了完全分散的自组织，它分布在系统的所有组件中。因此，自组织通常是有长期稳定的生存能力，在严重的干扰下能自我修复。<br /> <br /> [[混沌理论]]中讨论的自组织，就如同不可预测的大海中的确定性孤岛。<br /> <br /> <br /> <br /> 自组织主要出现在在物理，化学，生物，人工智能和认知系统等领域。其中的结晶，流体的热对流，化学振荡，动物种群，神经回路均与自组织息息相关。<br /> <br /> <br /> 自组织是在'''非平衡 Non-equilibrium '''过程的物理学和化学反应中被发现的，<ref name="G&P 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London.</ref>通常将其描述为'''自组装 Self-assembly '''。在生物学中，从分子到生态系统，这一概念已被证明是有效的。<ref name=":0">Compare: {{cite book| last1=Camazine| first1=Scott| title=Self-organization in Biological Systems| url=https://books.google.com/books?id=zMgyNN6Ufj0C| series=Princeton studies in complexity| edition=reprint| publisher=Princeton University Press| publication-date=2003| isbn=9780691116242| access-date=2016-04-05| year=2003}}</ref>在自然科学和社会科学，甚至在经济学和人类学的文献中也出现了自组织行为的引证。在诸如'''[[元胞自动机]] Cellular automata '''这样的数学系统中也观察到了自组织。<ref name=":1">{{cite book| last1=Ilachinski| first1=Andrew| title=Cellular Automata: A Discrete Universe| url=https://books.google.com/books?id=3Hx2lx_pEF8C| publisher=World Scientific| publication-date=2001| page=247| isbn=9789812381835| quote=We have already seen ample evidence for what is arguably the single most impressive general property of CA, namely their capacity for self-organization| year=2001}}</ref>自组织是与'''[[涌现 Emergence]] '''概念相关的一个例子。<ref>{{cite book |author=Feltz, Bernard |display-authors=etal |date=2006 |title=Self-organization and Emergence in Life Sciences |isbn=978-1-402-03916-4 |page=1}}</ref><br /> <br /> <br /> 自组织的四个基本要素如下：<ref>{{cite book |author1=Bonabeau, Eric |author2=Dorigo, Marco |author3=Theraulaz, Guy |date=1999 |title=Swarm intelligence: from natural to artificial systems |isbn=978-0-19-513159-8|publisher=OUP USA|pages=9–11|url=https://books.google.com/books?id=PvTDhzqMr7cC}}</ref><br /> #很强的动态分线性特性，通常都会涉及[[正反馈]]和负反馈，虽然不是必然<br /> #利用（已有的）和探测（未知的）之间的平衡<br /> #多重交互<br /> #能量的可用性（以克服'''[[熵增]] Entropy '''或无序的自然趋势）<br /> <br /> <br /> ==原理==<br /> [[控制论]]专家威廉·罗斯·阿什比 W. Ross Ashby 在1947年提出了'''自组织 Self-organization '''的初始原理，<ref name="ashby1947">{{Cite journal | doi=10.1080/00221309.1947.9918144| pmid=20270223| title=Principles of the Self-Organizing Dynamic System| journal=The Journal of General Psychology| volume=37| issue=2| pages=125–28| year=1947| last1=Ashby | first1=W. R.}}</ref><ref>Ashby, W. R. (1962). [http://csis.pace.edu/~marchese/CS396x/Computing/Ashby.pdf "Principles of the self-organizing system"], pp. 255–78 in ''Principles of Self-Organization''. Heinz von Foerster and George W. Zopf, Jr. (eds.) U.S. Office of Naval Research.</ref>它指出任何确定性[[动力系统]]都会自动演变成一个均衡状态，这种均衡状态可以描述为一个在盆地周围环绕状态的'''[[吸引子]] Attractor '''。一旦系统演化进入到吸引子中，系统的进一步演化就被约束，该系统将依存在吸引子中。这种约束代表了其组成元素或子系统之间相互依赖或协调的某种形式。用Ashby的话来说，每个子系统都适应了所有其他子系统形成的环境。<ref name=ashby1947/><br /> <br /> <br /> [[控制论]]专家海因茨·冯·福斯特 Heinz von Foerster 于1960年提出了“ 从噪声中获得有序 Order from noise ” 的原理。<ref>Von Foerster, H. (1960). [http://e1020.pbworks.com/f/fulltext.pdf "On self-organizing systems and their environments"], pp. 31–50 in ''Self-organizing systems''. M.C. Yovits and S. Cameron (eds.), Pergamon Press, London</ref> 该原理指出，自组织是由随机扰动 “噪声” 促进的，该随机扰动使系统在其状态空间中探索各种状态。这增加了系统到达“强”或“深”吸引子池中的机会，然后系统会迅速进入吸引子本身。生物物理学家亨利·阿特兰 Henri Atlan 通过提出“ 噪声带来的复杂性 Complexity from noise，法语 le principe de complexité par le bruit ” 原理发展了这一概念，<ref>See [https://www.google.com/search?&tbm=bks&q=inauthor:%22Henri+Atlan%22%22complexity+from+noise%22 occurrences] on Google Books.</ref><ref>{{cite book |editor-last=François |editor-first=Charles |editor-link= |title=International Encyclopedia of Systems and Cybernetics |year=2011 |origyear=[https://books.google.com/books?id=SZxnQgAACAAJ 1997] |edition=2nd |publisher=Walter de Gruyter |location=Berlin |page=[https://books.google.com/?id=XCn2mn98uEAC&pg=PA107&dq=%22complexity+from+noise+principle%22+Atlan+1972 107] |isbn=978-3-1109-6801-9 |title-link= }}</ref> 该原理首见于1972年出版的《L'organisation biologique et lathéoriede l'information》，<ref>[https://www.google.com/search?&q=%22complexité+par+le+bruit%22%22L'Organisation+biologique+et+la+théorie+de+l'information%22+1972].</ref> 然后是1979年出版的《Entre le cristal et lafumée》。<ref>Nicolis, G. and Prigogine, I. (1977). ''Self-organization in nonequilibrium systems: From dissipative structures to order through fluctuations''. Wiley, New York.</ref> 热力学家伊利亚·[[普利高津]] Ilya Prigogine 提出了类似的原则，即“波动带来有序 Order through fluctuations ”<ref>Nicolis, G. and Prigogine, I. (1977). ''Self-organization in nonequilibrium systems: From dissipative structures to order through fluctuations''. Wiley, New York.</ref> 或“混乱带来有序 Order out of chaos ”<ref>Prigogine, I. and Stengers, I. (1984). ''Order out of chaos: Man's new dialogue with nature''. Bantam Books.</ref>。它也应用在用于解决问题和机器学习的[[模拟退火]]方法中。<ref>{{cite journal |last1=Ahmed |first1=Furqan |title=Simulated annealing variants for self-organized resource allocation in small cell networks |journal=Applied Soft Computing |last2=Tirkkonen |first2=Olav |date=January 2016 |volume=38|pages=762–70 |doi=10.1016/j.asoc.2015.10.028 }}</ref><br /> <br /> ==历史演变==<br /> 系统动力演化可以自动形成组织的想法历史悠久。像德谟克里特 Democritus 和卢克雷修斯 Lucretius 之类的古代[https://en.wikipedia.org/wiki/Atomism 原子论者]认为，一种有计划的智能对于在自然界中创造有序是不必要的，他们认为，只要有足够的时间、空间和物质，有序就会自动产生。<ref>{{cite book |last1 =Palmer |first1= Ada |author-link1= Ada Palmer |title= Reading Lucretius in the Renaissance |date= October 2014|publisher= Harvard University Press |isbn= 978-0-674-72557-7|quote= Ada Palmer explores how Renaissance readers, such as Machiavelli, Pomponio Leto, and Montaigne, actually ingested and disseminated Lucretius, ... and shows how ideas of emergent order and natural selection, so critical to our current thinking, became embedded in Europe’s intellectual landscape before the seventeenth century. |url= http://www.hup.harvard.edu/catalog.php?isbn=9780674725577}}</ref><br /> <br /> <br /> 哲学家勒内·笛卡尔 René Descartes 在其1637年《方法论》的第五部分中假设性提出了'''自组织 Selft-organization '''的概念。他在未发表的作品《世界》中详细阐述了这个想法。<br /> <br /> <br /> 依曼纽尔·康德 Immanuel Kant 在他的1790年《审判批判》中使用了'''“自组织化 Selft-onganizing”'''一词，他认为只有存在这样的实体——其各个部分或“器官 Organs ”同时是终点和手段时——才是有意义的概念。这样的器官系统一定能够像拥有自己的思想一样行事，也就是说，它能够自我支配。<ref name="Kant">{{cite book|title= German Aesthetic|url= https://books.google.com/books?id=eC88AAAAIAAJ&pg=PA64|publisher= CUP Archive|pages= 64–|id= GGKEY:TFTHBB91ZH2}}</ref><br /> <br /> <br /> ''“在这样的天然产物中，其每一个部件都因其他剩余部件的存在而存在，也可以说它的存在是为了其他部件和整个整体，这是作为一种手段，或器官……该部件必须是可以产生其他部件的器官——因此每个部件都会相互产生其他部件……只有在这些条件和关系下，这样的产物才能成为一个系统的和自组织的存在，而且因此才能被称为一个物理结束。”''<ref name=Kant/><br /> <br /> <br /> 萨迪·卡诺 Sadi Carnot，1796-1832 和鲁道夫·克劳修斯 Rudolf Clausius，1822-1888 在19世纪发现了热力学第二定律。它指出：总的熵，有时被理解为无序，在一个孤立的系统中总会随着时间而增加。这意味着，如果没有外部联系降低系统中其他部位的'''有序 Order ''' 例如，通过消耗电池的低熵能量来扩散高熵热，那么系统无法自发地增加'''有序。<ref>Nicolas Léonard Sadi Carnot|Carnot, S. (1824/1986). [http://www.worldcat.org/title/reflections-on-the-motive-power-of-fire-a-critical-edition-with-the-surviving-scientific-manuscripts-translated-and-edited-by-fox-robert/oclc/812944517&referer=brief_results ''Reflections on the motive power of fire''], Manchester University Press, Manchester UK</ref><ref>{{cite journal |last= Clausius |first= R. |author1-link= |title= Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten Lassen |journal= Annalen der Physik |year= 1850|volume= 79 |issue= 4 |pages= 368–97, 500–24 |url= http://gallica.bnf.fr/ark:/12148/bpt6k15164w/f518.image |doi= 10.1002/andp.18501550403 |bibcode = 1850AnP...155..500C |hdl= 2027/uc1.$b242250 |hdl-access= free }} Translated into English: {{cite journal|last= Clausius |first= R. |title= On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom|journal= London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |date= July 1851 |volume= 2 |series= 4th |issue= VIII |pages= 1–21, 102–19 |url= https://archive.org/stream/londonedinburghd02lond#page/1/mode/1up|accessdate= 26 June 2012|doi= 10.1080/14786445108646819 }}</ref><br /> <br /> <br /> 18世纪的思想家试图理解“形式的普遍定律 Universal laws of form ”，以解释观察到的生物体形式。这个想法与'''拉马克主义 Lamarckism '''联系在一起，并声名狼藉，直到20世纪初 D'Arcy Wentworth Thompson 1860–1948 试图复兴它。<ref name="Ruse">{{cite book |author1= Ruse, Michael |editor1-last= Henning |editor1-first= Brian G. |editor2-last= Scarfe |editor2-first= Adam |title= Beyond Mechanism: Putting Life Back Into Biology |date= 2013 |publisher= Lexington Books |page= 419 |url= https://books.google.com/books?id=3VtosxAtq-EC|chapter= 17. From Organicism to Mechanism-and Halfway Back?|isbn= 9780739174371 }}</ref><br /> <br /> <br /> 精神病学家和工程师 Ashby 于1947年向当代科学引入了'''“自组织 Self-organizing”'''一词。<ref name=ashby1947/> 控制论学者 Heinz von Foerster，戈登·帕斯克 Gordon Pask ，斯塔福德·比尔 Stafford Beer 采纳了这一概念，Heinz von Foerster于1960年6月在伊利诺伊大学阿勒顿公园组织了一次有关“自组织原理 The Principles of Self-Organization ”的会议，该会议引发了一系列关于自组织系统的会议。<ref>Asaro, P. (2007). [http://peterasaro.org/writing/Asaro%20HVF%26BCL.pdf "Heinz von Foerster and the Bio-Computing Movements of the 1960s"] in Albert Müller and Karl H. Müller (eds.) ''An Unfinished Revolution? Heinz von Foerster and the Biological Computer Laboratory'' BCL 1958–1976. Vienna, Austria: Edition Echoraum.</ref> 诺伯特·维纳 Norbert Wiener在他的《控制论》第二版中提出了这个想法：《动物与机器中的控制与通讯》 1961 。<br /> <br /> <br /> '''自组织 Self-organization '''与60年代的一般系统理论相关，但是直到物理学家 Hermann Haken等人和复杂系统的研究者从更大范围采纳了这一概念才在科学文献中变得司空见惯起来，这些范围包括宇宙学家埃里希•詹茨 Erich Jantsch ，耗散系统的化学，具备系统思维兴起于1980年代圣塔菲学院 Santa Fe Institute和1990年代复杂适应系统的'''自创生 Autopoiesis '''机制的生物学和社会学领域，以及如今受'''根茎网络理论 Rhizomatic network theory '''深刻影响而出现的颠覆性技术。<ref><br /> As an indication of the increasing importance of this concept, when queried with the keyword <tt>self-organ*</tt>, ''Dissertation Abstracts'' finds nothing before 1954, and only four entries before 1970. There were 17 in the years 1971–1980; 126 in 1981–1990; and 593 in 1991–2000.<br /> </ref><br /> <br /> <br /> 在2008-2009年，'''引导式自组织 Guided self-organization '''的概念开始形成。这种方法旨在针对特定目的调整自组织，以便动态系统可以达到特定的吸引子或结果。这种调整通过限制系统组件之间的局部相互作用，而不是依靠一种明确的控制机制或全局设计蓝图，来限制复杂系统中的自组织过程。通过将任务无关的全局目标与任务相关的对局部相互作用的约束相结合，可以实现预期的结果，例如增加由此带来的内部结构和/或功能。<ref>Phys.org, [https://phys.org/news/2014-02-self-organizing-robots-robotic-crew-foreman.html Self-organizing robots: Robotic construction crew needs no foreman (w/ video)], February 13, 2014.</ref><ref>Science Daily, [https://www.sciencedaily.com/releases/2015/10/151027123342.htm Robotic systems: How sensorimotor intelligence may develop... self-organized behaviors ], October 27, 2015.</ref><br /> <br /> ==按领域==<br /> ===物理===<br /> [[File:ConvectionCells.png|300px|thumb|引力场中的对流单元|right]]<br /> 物理学中的自组织现象包括'''[[相变]] Phase transitions '''和'''自发对称性破缺 Spontaneous symmetry breaking '''，例如'''自发磁化 Spontaneous magnetization ''' ，经典物理学中的晶体生长，激光，<ref>Zeiger, H. J. and Kelley, P. L. (1991) "Lasers", pp. 614–19 in ''The Encyclopedia of Physics'', Second Edition, edited by Lerner, R. and Trigg, G., VCH Publishers.</ref> 超导和量子物理学的'''玻色-爱因斯坦凝聚 Bose–Einstein condensation '''。它在动力学系统，摩擦学，'''自旋泡沫系统 Spin foam systems '''和'''环量子引力 Loop quantum gravity '''<ref>Ansari M. H. (2004) [https://arxiv.org/abs/hep-th/0412307 Self-organized theory in quantum gravity]. arxiv.org</ref> 的'''自组织临界 Self-organized criticality '''中被发现，也在河流盆地和三角洲，'''枝晶凝固 Dendritic solidification （如雪花） '''和'''湍流结构 Turbulent structure '''中被发现。<ref name=":0" /><ref name=":1" /><br /> <br /> <br /> ===化学===<br /> [[File:DNA_nanostructures.png|300px|thumb|左侧示意的DNA结构自组装为右侧的结构|right]]<br /> 化学中的自组织包括分子'''自组装 Molecular self-assembly'''，<ref>{{cite journal|author=Lehn, J.-M. |journal=|title=Perspectives in Supramolecular Chemistry-From Molecular Recognition towards Molecular Information Processing and Self-Organization |volume=27 |issue=11 |year=1988 |pages=89–121 |doi=10.1002/anie.198800891}}</ref> '''反应扩散系统 Reaction–diffusion systems''' 和'''振荡反应 Oscillating reactions'''，<ref>{{cite journal | doi=10.1021/ja01439a007 | year=1921 | author=Bray, William C. | journal=Journal of the American Chemical Society | volume=43 | pages=1262–67 | issue=6 |title=A periodic reaction in homogeneous solution and its relation to catalysis.}}</ref> '''自催化网络 Autocatalytic networks'''，'''液晶 Liquid crystals'''，<ref>{{cite journal |url=http://www.csupomona.edu/~jarego/pubs/RD2_LC.pdf |title=Asymmetric synthesis of a highly soluble 'trimeric' analogue of the chiral nematic liquid crystal twist agent Merck S1011 |last=Rego |first=J.A. |last2=Harvey |first2=Jamie A.A. |last3=MacKinnon |first3=Andrew L. |last4=Gatdula |first4=Elysse |journal=Liquid Crystals |volume=37 |issue=1 |date=January 2010 |pages=37–43 |doi=10.1080/02678290903359291 |url-status=dead |archiveurl=https://www.webcitation.org/5oxBzwQCm?url=http://www.csupomona.edu/~jarego/pubs/RD2_LC.pdf |archivedate=2010-04-13}}</ref> '''网格络合物 Ggrid complexes'''，'''胶质晶体 Colloidal crystals'''，'''自组装单分子层 Self-assembled monolayers'''，<ref>{{cite journal|last1=Love|title= Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology |journal=Chem. Rev. |year=2005 |volume=105 |pages=1103–70 |doi=10.1021/cr0300789 |last2=Estroff |first2=Lara A. |last3=Kriebel |first3=Jennah K.|last4=Nuzzo|first4=Ralph G. |last5=Whitesides |first5=George M. |pmid=15826011 |issue=4 |displayauthors= 1}}</ref><ref name="Raval2003">{{cite journal|last=Barlow |first=S.M.|author2=Raval R.. |title=Complex organic molecules at metal surfaces: bonding, organisation and chirality |journal=Surface Science Report |year=2003 |volume=50 |issue=6–8 |pages=201–341 |doi=10.1016/S0167-5729(03)00015-3 |bibcode=2003SurSR..50..201B }}</ref>'''胶束 Micelles'''，'''嵌段共聚物的微相分离 Microphase separation of block copolymers''' 和'''Langmuir-Blodgett膜 Langmuir–Blodgett films'''。<ref>{{Cite journal | doi=10.1038/srep34095 | title=Large Area Fabrication of Semiconducting Phosphorene by Langmuir-Blodgett Assembly| journal=Sci. Rep.| volume=6| page=34095| year=2016| last1=Ritu | first1=Harneet | pmid=27671093 | pmc=5037434| arxiv=1605.00875| bibcode=2016NatSR...634095K}}</ref><br /> <br /> <br /> ===生物===<br /> [[File:birds.jpg|300px|thumb|鸟类蜂群，生物学中的自我组织的一个例子|right]]<br /> 在生物学中<ref>Camazine, Deneubourg, Franks, Sneyd, Theraulaz, Bonabeau, ''Self-Organization in Biological Systems'', Princeton University|Princeton University Press, 2003.</ref>，从蛋白质和其它生物大分子的'''自发折叠 Spontaneous folding'''，'''磷脂双分子层 Lipid bilayer '''的形成，发育生物学的'''图案形成 Pattern formation'''和'''形态发生 Morphogenesis'''，人体运动的协调，群居昆虫如蜜蜂，蚂蚁，白蚁<ref>{{cite journal|last1=Bonabeau|first1=Eric |display-authors=etal |title=Self-organization in social insects|journal=Trends in Ecology & Evolution|date=May 1997|volume=12|issue=5|pages=188–93|doi=10.1016/S0169-5347(97)01048-3|pmid=21238030 |url=https://dipot.ulb.ac.be/dspace/bitstream/2013/19269/1/020BonabeauTrendsEcologyEvolution97.pdf }}</ref> 和哺乳动物的社会行为，到鸟类和鱼类的'''群集行为 Flocking behaviour'''，都可以观察到自组织现象。<ref>{{cite journal |last1=Couzin |first1=Iain D. |last2=Krause |first2=Jens |title=Self-Organization and Collective Behavior in Vertebrates |journal=Advances in the Study of Behavior |date=2003 |volume=32 |pages=1–75 |url=http://icouzin.princeton.edu/wp-content/uploads/file/PDFs/Couzin%20and%20Krause,%202003.pdf |url-status=dead |archiveurl=https://web.archive.org/web/20161220075600/http://icouzin.princeton.edu/wp-content/uploads/file/PDFs/Couzin%20and%20Krause,%202003.pdf |archivedate=2016-12-20|doi=10.1016/S0065-3454(03)01001-5 |isbn=9780120045327 }}</ref><br /> <br /> <br /> 数学生物学家斯图尔特·考夫曼 Stuart Kauffman 和其他结构主义者认为，自组织可能与自然选择在进化生物学的三个领域中共同发挥作用，即'''种群动力学 Population dynamics'''，'''分子进化 Molecular evolution '''和'''形态发生 Morphogenesis'''。但是，这种假设没有考虑能量在驱动细胞中生化反应中的重要作用。任何细胞中的反应系统都是'''自催化 Self-catalyzing'''的，但不是简单的自组织，因为它们是依赖于持续能量输入的热力学开放系统。<ref>{{cite journal |last1=Fox |first1=Ronald F. |title=Review of Stuart Kauffman, The Origins of Order: Self-Organization and Selection in Evolution |journal=Biophys. J. |date=December 1993 |volume=65 |issue=6 |pages=2698–99 |pmc=1226010 |doi=10.1016/s0006-3495(93)81321-3 |bibcode=1993BpJ....65.2698F}}</ref><ref>{{cite book |author=Goodwin, Brian |authorlink=|title=Beyond the Darwinian Paradigm: Understanding Biological Forms |work=Evolution: The First Four Billion Years |editor1=Ruse, Michael |editor1link=Michael Ruse |editor2=Travis, Joseph |publisher=Harvard University Press |date=2009}}</ref> 自组织不是自然选择的替代方法，但是它限制了进化可以做什么，并提供了诸如膜的自组装之类的机制，以便进化利用这种机制。<ref>{{cite journal |last1=Johnson |first1=Brian R. |last2=Lam |first2=Sheung Kwam |title=Self-organization, Natural Selection, and Evolution: Cellular Hardware and Genetic Software |journal=BioScience |date=2010|volume=60 |issue=11 |pages=879–85 |doi=10.1525/bio.2010.60.11.4 |url=http://bioscience.oxfordjournals.org/content/60/11/879.full}}</ref><br /> <br /> <br /> ===计算机科学===<br /> 来自数学和计算机科学的现象，例如'''[[元胞自动机]] Cellular automata'''，'''[[随机图]] Random graphs'''，以及'''进化计算 Evolutionary computation '''和'''人工生命 Artificial life '''的某些实例，都表现出了自组织的特征。在群体机器人 Swarm robotics 中，自组织被用来产生涌现行为 Emergent behavior。尤其是随机图理论作为复杂系统的一般原理，已被用作自组织的正当理由。在多主体系统领域，理解如何设计一个能够表现出自组织行为的系统是一个活跃的研究领域。<ref>{{cite journal|last1=Serugendo |first1=Giovanna Di Marzo |display-authors=etal |title=Self-organization in multi-agent systems |journal=Knowledge Engineering Review|date=June 2005|volume=20|issue=2|pages=165–89|doi=10.1017/S0269888905000494|url=https://archive-ouverte.unige.ch/unige:120878 }}</ref>优化算法也可以认为是自组织化 Self-organizing的，因为它们旨在找到问题的最优解。如果将这个解视为迭代系统的一个状态，则最优解是系统选定的收敛结构。<ref>{{Cite journal | doi=10.1007/s00521-013-1498-4| title=A framework for self-tuning optimization algorithm| journal=Neural Computing and Applications| volume=23| issue=7–8| pages=2051–57| year=2013| last1=Yang | first1=X. S. | last2=Deb | first2=S. | last3=Loomes | first3=M. | last4=Karamanoglu | first4=M. | arxiv=1312.5667| bibcode=2013arXiv1312.5667Y}}</ref><ref>X. S. Yang (2014) ''Nature-Inspired Optimization Algorithms'', Elsevier.</ref> 自组织网络包括''' [[小世界网络]] Small-world networks '''<ref>{{cite journal|last1=Watts|first1=Duncan J.|last2=Strogatz|first2=Steven H.|title=Collective dynamics of 'small-world' networks|journal=Nature|date=June 1998|volume=393|issue=6684|pages=440–42|doi=10.1038/30918|pmid=9623998|bibcode=1998Natur.393..440W}}</ref> 和''' [[无标度网络]] Scale-free networks'''。它们来自自下而上的相互作用，这与组织内部的自上而下的层次网络不同，后者不是自组织的。<ref name="Clauset">{{Cite journal | doi=10.1137/070710111| last=Clauset| first=Aaron| author2=Cosma Rohilla Shalizi |author3=M. E. J Newman | title=Power-law distributions in empirical data| journal=SIAM Review| year=2009| arxiv=0706.1062 |bibcode=2009SIAMR..51..661C | volume=51 | issue=4| pages=661–703}}</ref> 有人认为云计算系统本质上也是自组织的，<ref>{{Cite journal|last=Zhang, Q., Cheng, L., and Boutaba, R.|date=2010|title=Cloud computing: state-of-the-art and research challenges|journal=Journal of Internet Services and Applications|volume=1|issue=1|pages=7–18|doi=10.1007/s13174-010-0007-6|doi-access=free}}</ref> 但尽管它们具有一定的自治性，它们并不是自我管理的，因为它们的目标不是降低自身的复杂性。<ref>{{Cite arxiv|last1=Marinescu |first1=D. C. |last2=Paya |first2=A. |last3=Morrison |first3=J. P. |last4=Healy |first4=P. |date=2013|title=An auction-driven self-organising cloud delivery model |eprint=1312.2998|class=cs.DC }}</ref><ref>{{Cite journal|last=Lynn |display-authors=etal |date=2016 |title=Cloudlightning: A Framework for a Self-organising and Self-managing Heterogeneous Cloud |url=http://www.scitepress.org/DigitalLibrary/PublicationsDetail.aspx?ID=cHtD7x49Rn8=&t=1 |journal=Proceedings of the 6th International Conference on Cloud Computing and Services Science|page=333 |doi=10.5220/0005921503330338|isbn=978-989-758-182-3|doi-access=free }}</ref><br /> <br /> <br /> ===控制论===<br /> 诺伯特·维纳认为黑盒的'''自动串行识别 Automatic serial identification '''及其随后的'''复制 reproduction '''作为控制论中的自组织。<ref>Wiener, Norbert (1962) "The mathematics of self-organising systems". ''Recent developments in information and decision processes'', Macmillan, N. Y. and Chapter X in ''Cybernetics, or control and communication in the animal and the machine'', The MIT Press.</ref>维纳所称的'''锁相 Phase locking '''或'''“频率吸引 Attraction of frequencies”'''的重要性在他的《控制论——动物与机器中的控制与通信》第二版中进行了讨论。<ref>''Cybernetics, or control and communication in the animal and the machine'', The MIT Press, Cambridge, Massachusetts and Wiley, NY, 1948. 2nd Edition 1962 "Chapter X "Brain Waves and Self-Organizing Systems" pp. 201–02.</ref> 埃里克·德雷克斯勒 K. Eric Drexler 将'''自我复制 Self-replication '''视为纳米和'''通用组装 universal assembly '''的关键步骤。<ref>William Ross Ashby|Ashby, William Ross](1952) ''Design for a Brain'', Chapter 5 Chapman & Hall</ref>相比之下，当 Ross Ashby 的同态调节器——四个同时连通的检流计——受到干扰时，会收敛于许多可能的稳定状态之一。Ross Ashby使用各种状态计数方法来描述稳定状态，并推导出'''“良好调节器 Good Regulator ”''' 定理，<ref>{{cite journal|title=Every good regulator of a system must be a model of that system |author=Conant, R. C.|author2=Ashby, W. R. |journal=Int. J. Systems Sci.|volume=1 |issue=2 |pages=89–97 |year=1970 |url=http://pcp.vub.ac.be/Books/Conant_Ashby.pdf |doi=10.1080/00207727008920220}}</ref> 该定理要求内部模型具有自组织的持久性和稳定性。例如，'''奈奎斯特稳定性标准 Nyquist stability criterion'''。沃伦·麦卡洛克 Warren McCulloch 提出的'''“潜在命令冗余 Redundancy of Potential Command”'''，是大脑和人类神经系统组织的特征，也是自组织的必要条件。Heinz von Foerster提出了'''“冗余度 Redundancy”'''，<math>R=1-H /H_{max}</math>，其中<math>H</math>是熵。<ref>{{cite journal|author=von Foerster, Heinz |author2= Pask, Gordon |title=A Predictive Model for Self-Organizing Systems, Part I|journal=Cybernetica|volume= 3|pages= 258–300|year=1961}}</ref><ref>{{cite journal|author=von Foerster, Heinz |author2= Pask, Gordon |title=A Predictive Model for Self-Organizing Systems, Part II|journal=Cybernetica|volume= 4 |pages=20–55|year= 1961}}</ref> 本质上，这表明未使用的潜在通信带宽是对自组织的一种度量。<br /> <br /> <br /> 1970年代，Stafford Beer 认为自组织对于持久的生命系统的自治是必要的。他将'''活性系统模型 viable system model'''应用于管理。它由五个部分组成：<br /> #监视生存过程的表现<br /> #通过规则的递归应用进行管理<br /> #稳态操作控制<br /> #开发 <br /> #使得在环境干扰下依然可维持身份<br /> <br /> <br /> 通过警报“algedonic loop”反馈来优选焦点：这种反馈是一种对相对于标准功能表现不足或超出表现所产生的疼痛和愉悦的敏感性。<ref>"Brain of the Firm" Alan Lane (1972); see also Viable System Model in "Beyond Dispute", and Stafford Beer (1994) "Redundancy of Potential Command" pp. 157–58.</ref><br /> <br /> <br /> 在1990年代，Gordon Pask 辩称，von Foerster 的H和Hmax不是独立的，而是通过可数的'''无限递归并发自旋过程 Countably infinite recursive concurrent spin processes '''相互作用的，<ref name=p1996/> 他称之为概念。他严格定义了“建立关系的程序 A procedure to bring about a relation”这一概念，<ref name=p1973/> 使得他的定理“相似概念排斥，不同概念吸引 Like concepts repel, unlike concepts attract” ，<ref>{{Cite journal | doi=10.1108/03684920110391913| title=On Gordon Pask| journal=Kybernetes| volume=30| issue=5/6| pages=673–82| year=2001| last1=Green | first1=N. }}</ref> 以得出一种通用的、基于自旋的自组织原理。他的原则是一项排除原则，“ 非二重性 There are No Doppelgangers ”意味着没有两个概念完全相同。经过足够的时间后，所有概念都会吸引并合并成为粉红噪音 Pink noise。<ref>Pask, Gordon (1993) [http://www.cybsoc.org/PasksIAT.PDF ''Interactions of Actors (IA), Theory and Some Applications''].</ref><ref name="p1996">{{cite journal |author=Pask, Gordon |year=1996 |url=http://www.cybsoc.org/GPprog.PDF |title=Heinz von Foerster's Self-Organisation, the Progenitor of Conversation and Interaction Theories |journal= Systems Research |volume=13|issue= 3 |pages=349–62 |doi=10.1002/(sici)1099-1735(199609)13:3<349::aid-sres103>3.3.co;2-7}}</ref>该理论应用于可以产生持久、连贯产品的所有组织封闭 Organizationally closed 或体内平衡 Homeostatic 的过程，这些产品会不断发展，学习和适应。<br /> <br /> <br /> ===人类社会===<br /> [[File:CIA_Map_of_International_illegal_drug_connections.gif|300px|thumb|国际毒品贩卖路线的社会自组织|right]]<br /> 社会动物的自组织行为和简单数学结构的自组织现象，都表明在人类社会中应该存在自组织。自组织的迹象通常是自组织物理系统所体现出的统计属性。社会学，经济学，行为金融学和人类学中存在很多这样的例子，比如'''临界质量 Critical mass'''，'''羊群效应 Herd behaviour'''，'''集体思维 Groupthink '''等。<ref>''[http://cmol.nbi.dk/models/ Interactive models for self organization and biological systems]'' Center for Models of Life, Niels Bohr Institute, Denmark</ref><br /> <br /> <br /> 在社会理论中，尼古拉斯·卢曼 Niklas Luhmann 1984 引入了'''自我指涉 Self-referentiality'''的概念作为自组织理论的社会学应用。对于卢曼而言，社会系统的要素是'''自我再生产 Self-producing '''的交流，即交流产生进一步的交流，因此，只要存在不断变化的交流，社会系统就可以自我复制。对于卢曼而言，人类就是系统环境中的传感器。卢曼通过'''功能分析 Functional analyses '''和系统理论发展出一套关于社会及其子系统的进化论。<ref>Niklas Luhmann|Luhmann, Niklas (1995) ''Social Systems''. Stanford, California: Stanford University Press. </ref><br /> <br /> <br /> 在经济学中，市场经济有时被认为是自组织的。保罗·克鲁格曼 Paul Krugman 在他的著作《自组织经济 The Self Organizing Economy》中阐述了市场自组织在商业周期中的作用。弗里德里希·哈耶克 Friedrich Hayek 创造了术语'''“ 耦合秩序 catallaxy” '''，以描述一种'''“自愿合作的自组织系统 Self-organizing system of voluntary co-operation”''',这与自由市场经济中的自发秩序有关。新古典经济学家认为，加强中央计划通常会使自组织的经济体系效率降低。从另一个角度来看，经济学家认为市场失灵如此明显以至于自组织产生了不良结果，因此国家应指导生产和定价。大多数经济学家都采取中间立场，并建议将市场经济和'''计划经济 Command economy '''的特征混合在一起有时称为'''混合经济 Mixed economy '''。当应用在经济学领域时，自组织的概念很容易变成一种意识形态上的渗透。<ref name="Biel2009">{{Cite journal| author=Biel, R. |author2=Mu-Jeong Kho |url=http://rechercheregulation.files.wordpress.com/2013/01/rr_working_serieid_2009-1.pdf |title=The Issue of Energy within a Dialectical Approach to the Regulationist Problematique |journal=Recherches & Régulation Working Papers, RR Série ID 2009-1 |pages=1–21 |publisher=Association Recherche & Régulation |date=November 2009 |accessdate=2013-11-09}}</ref><ref>Alan Marshall (New Zealand author)|Marshall, A.(2002) ''The Unity of Nature'', Chapter 5. Imperial College Press. </ref><br /> <br /> <br /> ===学习领域===<br /> 使他人“学习如何学习”<ref>Rogers.C. (1969). ''Freedom to Learn''. Merrill</ref> 通常是指教导他们如何服从于被教导。'''自组织学习 Self-organised learning, SOL '''<ref>Thomas L.F. & Augstein E.S. (1985) ''Self-Organised Learning: Foundations of a conversational science for psychology''. Routledge (1st Ed.)</ref><ref>Thomas L.F. & Augstein E.S. (1994) ''Self-Organised Learning: Foundations of a conversational science for psychology''. Routledge (2nd Ed.)</ref><ref>Thomas L.F. & Augstein E.S. (2013) ''[https://books.google.com/books?id=xWVcDQAAQBAJ&printsec=frontcoverSelf-Organised Learning: Foundations of a conversational science for psychology]''. Routledge (Psy. Revivals)</ref> 否认“专家最了解”或存在“最佳方法”，<ref>Harri-Augstein E. S. and Thomas L. F. (1991) ''Learning Conversations: The S-O-L way to personal and organizational growth''. Routledge (1st Ed.)</ref><ref>Harri-Augstein E. S. and Thomas L. F. (2013) ''Learning Conversations: The S-O-L way to personal and organizational growth''. Routledge (2nd Ed.)</ref><ref>Harri-Augstein E. S. and Thomas L. F. (2013)''Learning Conversations: The S-O-L way to personal and organizational growth''. BookBaby (eBook)</ref> 反而坚持认为“个体层面显著的、相关的和可行意义的建构”，<ref>Illich. I. (1971) ''A Celebration of Awareness''. Penguin Books.</ref> 应由学习者进行体验性尝试。<ref>Harri-Augstein E. S. (2000) ''The University of Learning in transformation''</ref> 这可能是协作完成的，而且个人收获更大。<ref>Schumacher, E. F. (1997) ''This I Believe and Other Essays (Resurgence Book)''. </ref><ref>Revans R. W. (1982) ''The Origins and Growth of Action Learning'' Chartwell-Bratt, Bromley</ref> 它被视为一生的过程，并不受限于特定的学习环境家庭，学校，大学，也不受限于父母或教授等权威机构的控制。<ref>Thomas L.F. and Harri-Augstein S. (1993) "On Becoming a Learning Organisation" in ''Report of a 7 year Action Research Project with the Royal Mail Business''. CSHL Monograph</ref> 它需要通过学习者的亲身经历去尝试、并且不断去修正。<ref>Rogers C.R. (1971) ''On Becoming a Person''. Constable, London</ref> 它也不必受限于意识或语言。<ref>Prigogyne I. & Sengers I. (1985) ''Order out of Chaos'' Flamingo Paperbacks. London</ref>弗里特霍夫·卡普拉 Fritjof Capra 声称，这自组织学习，在心理学和教育中鲜为人知。<ref>Capra F (1989) ''Uncommon Wisdom'' Flamingo Paperbacks. London</ref> 它可能与控制论有关，<ref name=p1973>Pask, G. (1973). ''Conversation, Cognition and Learning. A Cybernetic Theory and Methodology''. Elsevier</ref><ref>Bohm D. (1994) ''Thought as a System''. Routledge.</ref>因为它涉及'''负反馈控制回路 Negative feedback control loop。'''它可以作为学习谈话或对话在学习者之间或一个人进行。<ref>Maslow, A. H. (1964). ''Religions, values, and peak-experiences'', Columbus: Ohio State University Press.</ref><ref>''Conversational Science'' Thomas L.F. and Harri-Augstein E.S. (1985)</ref><br /> <br /> <br /> ===交通流===<br /> 交通流中驾驶员的自组织行为几乎决定了交通的所有时空行为，例如高速公路瓶颈处的交通故障，高速公路通行能力以及交通拥堵的出现。在1996–2002年，鲍里斯·克纳 Boris Kerner 的三相交通理论解释了这些复杂的自组织效应。<ref>{{cite journal | last1 = Kerner | first1 = Boris S. | year = 1998 | title = Experimental Features of Self-Organization in Traffic Flow | journal = Physical Review Letters | volume = 81| issue = 17 | pages = 3797–3800| doi=10.1103/physrevlett.81.3797 | bibcode=1998PhRvL..81.3797K}}</ref><br /> <br /> <br /> ===语言学===<br /> 随着个体和群体行为与生物进化相互作用，秩序在语言的进化中自发出现。<ref>{{cite book |last1=De Boer|first1=Bart |title=Self-organization and language evolution |work=The Oxford Handbook of Language Evolution |editor=Gibson, Kathleen R. |editor2=Tallerman, Maggie |date=2011 |publisher=Oxford}}</ref><br /> <br /> <br /> ===研究基金===<br /> 自组织拨款 Self-organized funding allocation，SOFA 是为科学研究分配资金的一种方法。在这个系统中，每个研究人员都被分配了相等数量的资金，并且被要求匿名分配他们一部分资金用于其他人的研究。SOFA的支持者认为，这将导致与目前的拨款系统相似的资金分配，但开销却更少。2016年，SOFA的测试试点在荷兰开始。<ref>{{cite journal |last1=Bollen |first1=Johan |title=Who would you share your funding with? |journal=Nature |date=8 August 2018 |volume=560 |issue=7717 |pages=143 |doi=10.1038/d41586-018-05887-3 |pmid=30089925 |language=EN|bibcode=2018Natur.560..143B |doi-access=free }}</ref> In 2016, a test pilot of SOFA began in the Netherlands.<ref>{{cite web |last1=Coelho |first1=Andre |title=NETHERLANDS: A radical new way do fund science {{!}} BIEN |url=https://basicincome.org/news/2017/05/netherlands-radical-new-way-fund-science/ |accessdate=2 June 2019}}</ref><br /> <br /> ==批判==<br /> 海因茨·佩格尔斯 Heinz Pagels 在1985年对伊利亚·普里戈金 Ilya Prigogine和伊莎贝尔·斯滕格斯 Isabelle Stengers合著的《今日物理学中的秩序与混乱 Order Out of Chaos in Physics Today》一书的评论中呼吁权威：<ref>{{cite journal|url=http://www.fefox.com/ARTICLES/Pagels-PrigogineinPhysicsToday1985.pdf|author=Pagels, H. R. |title=Is the irreversibility we see a fundamental property of nature?|journal=Physics Today|volume=38 |issue=1 |date=January 1, 1985|pages=97–99|doi=10.1063/1.2813716|bibcode=1985PhT....38a..97P}}</ref><br /> <br /> <br /> ''大多数科学家会同意生物物理学家L. a . Blumenfeld在《生物物理学问题》（施普林格 Verlag, 1981）中表达的批判观点，他写道:“有意义的宏观生物结构的排序并不是由于某些参数或系统超过其临界值而产生的。”这些结构是按照类似复杂建筑结构的程序建造的，这些有意义的信息是在数十亿年的化学和生物进化过程中产生的。”生命是微观组织的结果，而不是宏观组织的结果。''<br /> <br /> 当然，Blumenfeld并没有进一步回答那些类似于程序的结构最初是如何出现的问题。他的解释直接导致了无限的倒退。<br /> <br /> <br /> ''简而言之，他们（Prigogine和Stengers）坚持认为，时间不可逆性不是来自于一个与时间无关的微观世界，而是它本身的根本。他们的想法的优点在于，它解决了他们所认为的关于物理中时间本质的“理论冲突”，使得大多数物理学家会同意。但既没有经验证据来支持他们的观点，也没有数学上的必要性，没有所谓的“教义冲突”，只有Prigogine和他的几个同事坚持这些推测。尽管他们作出了努力，这些推测仍然处于科学可信性的边缘地带。''<br /> <br /> <br /> 在神学方面，托马斯·阿奎那 Thomas Aquinas（1225-1274）在他的《神学总论 Summa Theologica》中否定了某物可以成为其自身组织的自给自足原因的观点，从而假定了一个目的性创造的宇宙：<ref>[http://www.newadvent.org/summa/1002.htm#article3 Article 3. Whether God exists?] newadvent.org</ref><br /> <br /> <br /> ''既然自然在一个更高的动因的指导下，为一个特定的目的而工作，那么自然所做的任何事情都必须追溯到上帝，追溯到它的最初的原因。因此，无论自愿做什么，也必须追溯到一些比人类理性或意志更高级的原因，因为这些原因可以改变或失败;因为所有可以改变的、有缺陷的事物都必须追溯到一个不可改变的、自我必须的第一原则，正如文章正文所示。''<br /> <br /> ==参阅==<br /> *[https://en.wikipedia.org/wiki/Autopoiesis 自创生 Autopoiesis]<br /> *[https://en.wikipedia.org/wiki/Autowave 自动波 Autowave]<br /> *[https://en.wikipedia.org/wiki/Self-organized_criticality_control 自组织的临界控制 Self-organized criticality control]<br /> *[https://en.wikipedia.org/wiki/Free_energy_principle 自由能原理 Free energy principle]<br /> *[[信息论 Information theory]]<br /> *[https://en.wikipedia.org/wiki/Adrian_Bejan#Constructal_law 构造法则 Constructal law]<br /> *[https://en.wikipedia.org/wiki/Swarm_intelligence 群体智能 Swarm intelligence]<br /> *[[蝴蝶效应 Butterfly effect]]<br /> <br /> ==参考文献==<br /> <references/><br /> <br /> <br /> ==编者推荐==<br /> [[File:3-1534215542.jpeg|300px|thumb|[https://swarma.org/?p=95 《Science Robotics：无人机的自组织飞行和集群智慧》]|right]]<br /> ===集智文章推荐===<br /> ====[https://swarma.org/?p=95 《Science Robotics：无人机的自组织飞行和集群智慧》]====<br /> 超级碗和奥运会开幕式上的无人机表演，都只是人为控制的程序，而在最近一期的 Science 子刊 Science Robitics 上，研究者经过算法优化和参数调节，让无人机群自发形成了非常优美的、自组织的集群行为。<br /> <br /> <br /> ====[https://swarma.org/?p=13286 《自愈路网：城市道路网交通事故的自组织管理策略 | 论文速递10篇》]====<br /> 交通拥堵有没有可能“自行治愈”？答案是肯定的，研究人员提出了一种新颖的自组织交通管理策略，一旦所有受影响的交通流量沿着剩余的道路容量重新分配，交通网络就会“自行治愈”。<br /> <br /> <br /> ====[https://swarma.org/?p=8883 《混合型社会：设计自组织系统集群行为的挑战及前景 | 复杂性文摘》]====<br /> 混合型社会是一种由不同组件组成的自组织的集群系统，这种自组织混合型社会面临哪些挑战？又有怎样的解决思路？<br /> <br /> <br /> ===课程推荐===<br /> ====[https://campus.swarma.org/play/coursedetail?id=10671 《自组织理论》]====<br /> 自组织现象的研究对象主要是复杂的自组织系统（生命系统，社会系统）的形成和发展机制问题，即在一定条件下，系统是如何自动地由无序走向有序，由低级有序走向宏结构和功能自发产生于自然界的许多领域中，我们能否获得统一普适的科学理解？本课程由北京师范大学系统科学学院教授狄增如亲授，帮助梳理了科学的发展脉络，介绍了时间反演对称、热力学第二定律及自组织现象的理论方法。<br /> <br /> <br /> ====[https://campus.swarma.org/play/coursedetail?id=11008 《结构与功能：从无序到有序》]====<br /> 系统科学中，有一条很重要的原理，就是系统结构和系统环境以及它们之间的关联关系，决定了系统整体性和功能。系统整体性与功能是内部系统结构与外部系统环境综合集成的结果，一个复杂系统的涌现特性的例子就是蚂蚁群体。另一个蚂蚁头脑简单，但是整个蚂蚁群体通过自组织而涌现出了高级复杂的蚂蚁社会结构。它们形成了非常明显的社会分工。本课程由北京师范大学系统科学学院教授李红刚亲授，一起探讨系统的结构与功能，聚焦于自组织涌现，如何从无序走向有序。<br /> <br /> <br /> ----<br /> 本中文词条由[[用户:木子二月鸟|木子二月鸟]]、[[用户:乐多多|乐多多]]用户参与编译，[[用户:苏格兰|苏格兰]]用户审校，[[用户:乐多多|乐多多]]编辑欢迎在讨论页面留言。<br /> <br /> <br /> '''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''<br /> [[Category:控制论]]<br /> [[Category:系统科学]]<br /> [[Category:自组织]]<br /> [[Category:物理概念]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E8%87%AA%E7%BB%84%E7%BB%87&diff=33924 自组织 2023-01-17T12:31:59Z

<p>TYcl20：</p> <hr /> <div>{{#seo:<br /> |keywords=自组织 Self-organization <br /> |description=也被称为自发秩序，是指一种起源于初始无序系统的部分元素之间的局部相互作用、所产生出某种形式的整体秩序的过程。 }}<br /> <br /> [[File:Nb3O7(OH)_self-organization2.jpg|400px|thumb|right|在200°C 的水热处理期间，微米级,<math>Nb_3O_7(OH)</math>立方体中的自组织。最初，无定形立方体逐渐转变为晶体纳米线的有序3D网格，如图模型所示。<ref>{{Cite journal | doi= 10.1039/C4TA02202E| title= Template-free synthesis of novel, highly-ordered 3D hierarchical Nb<sub>3</sub>O<sub>7</sub>(OH) superstructures with semiconductive and photoactive properties| journal= Journal of Materials Chemistry A| volume= 2| issue= 30| page= 12005| year= 2014| last1= Betzler | first1= S. B. | last2= Wisnet | first2= A. | last3= Breitbach | first3= B. | last4= Mitterbauer | first4= C. | last5= Weickert | first5= J. | last6= Schmidt-Mende | first6= L. | last7= Scheu | first7= C. |doi-access= free| url= https://kops.uni-konstanz.de/bitstream/123456789/28968/1/Betzler_289681.pdf}}</ref>]]<br /> '''自组织 Self-organization'''，在社会科学中也被称为[[自发秩序]]''Spontaneous order'' ，是指通过起源于初始无序系统的部分元素之间的局部发生相互作用，使某种形式的整体秩序形成的过程。当有足够的能量可用时，该过程可以是自发的，不需要任何外部主体进行控制。它是由看似随机的扰动触发的，并由正反馈放大，最终形成了完全分散的自组织，它分布在系统的所有组件中。因此，自组织通常是有长期稳定的生存能力，在严重的干扰下能自我修复。<br /> <br /> [[混沌理论]]中讨论的自组织，就如同不可预测的大海中的确定性孤岛。<br /> <br /> <br /> <br /> 自组织主要出现在在物理，化学，生物，人工智能和认知系统等领域。其中的结晶，流体的热对流，化学振荡，动物种群，神经回路均与自组织息息相关。<br /> <br /> <br /> 自组织是在'''非平衡 Non-equilibrium '''过程的物理学和化学反应中被发现的，<ref name="G&P 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London.</ref>通常将其描述为'''自组装 Self-assembly '''。在生物学中，从分子到生态系统，这一概念已被证明是有效的。<ref name=":0">Compare: {{cite book| last1=Camazine| first1=Scott| title=Self-organization in Biological Systems| url=https://books.google.com/books?id=zMgyNN6Ufj0C| series=Princeton studies in complexity| edition=reprint| publisher=Princeton University Press| publication-date=2003| isbn=9780691116242| access-date=2016-04-05| year=2003}}</ref>在自然科学和社会科学，甚至在经济学和人类学的文献中也出现了自组织行为的引证。在诸如'''[[元胞自动机]] Cellular automata '''这样的数学系统中也观察到了自组织。<ref name=":1">{{cite book| last1=Ilachinski| first1=Andrew| title=Cellular Automata: A Discrete Universe| url=https://books.google.com/books?id=3Hx2lx_pEF8C| publisher=World Scientific| publication-date=2001| page=247| isbn=9789812381835| quote=We have already seen ample evidence for what is arguably the single most impressive general property of CA, namely their capacity for self-organization| year=2001}}</ref>自组织是与'''[[涌现 Emergence]] '''概念相关的一个例子。<ref>{{cite book |author=Feltz, Bernard |display-authors=etal |date=2006 |title=Self-organization and Emergence in Life Sciences |isbn=978-1-402-03916-4 |page=1}}</ref><br /> <br /> <br /> 自组织的四个基本要素如下：<ref>{{cite book |author1=Bonabeau, Eric |author2=Dorigo, Marco |author3=Theraulaz, Guy |date=1999 |title=Swarm intelligence: from natural to artificial systems |isbn=978-0-19-513159-8|publisher=OUP USA|pages=9–11|url=https://books.google.com/books?id=PvTDhzqMr7cC}}</ref><br /> #很强的动态分线性特性，通常都会涉及[[正反馈]]和负反馈，虽然不是必然<br /> #利用（已有的）和探测（未知的）之间的平衡<br /> #多重交互<br /> #能量的可用性（以克服'''[[熵增]] Entropy '''或无序的自然趋势）<br /> <br /> <br /> ==原理==<br /> [[控制论]]专家威廉·罗斯·阿什比 W. Ross Ashby 在1947年提出了'''自组织 Self-organization '''的初始原理，<ref name="ashby1947">{{Cite journal | doi=10.1080/00221309.1947.9918144| pmid=20270223| title=Principles of the Self-Organizing Dynamic System| journal=The Journal of General Psychology| volume=37| issue=2| pages=125–28| year=1947| last1=Ashby | first1=W. R.}}</ref><ref>Ashby, W. R. (1962). [http://csis.pace.edu/~marchese/CS396x/Computing/Ashby.pdf "Principles of the self-organizing system"], pp. 255–78 in ''Principles of Self-Organization''. Heinz von Foerster and George W. Zopf, Jr. (eds.) U.S. Office of Naval Research.</ref>它指出任何确定性[[动力系统]]都会自动演变成一个均衡状态，这种均衡状态可以描述为一个在盆地周围环绕状态的'''[[吸引子]] Attractor '''。一旦系统演化进入到吸引子中，系统的进一步演化就被约束，该系统将依存在吸引子中。这种约束代表了其组成元素或子系统之间相互依赖或协调的某种形式。用Ashby的话来说，每个子系统都适应了所有其他子系统形成的环境。<ref name=ashby1947/><br /> <br /> <br /> [[控制论]]专家海因茨·冯·福斯特 Heinz von Foerster 于1960年提出了“ 从噪声中获得有序 Order from noise ” 的原理。<ref>Von Foerster, H. (1960). [http://e1020.pbworks.com/f/fulltext.pdf "On self-organizing systems and their environments"], pp. 31–50 in ''Self-organizing systems''. M.C. Yovits and S. Cameron (eds.), Pergamon Press, London</ref> 该原理指出，自组织是由随机扰动 “噪声” 促进的，该随机扰动使系统在其状态空间中探索各种状态。这增加了系统到达“强”或“深”吸引子池中的机会，然后系统会迅速进入吸引子本身。生物物理学家亨利·阿特兰 Henri Atlan 通过提出“ 噪声带来的复杂性 Complexity from noise，法语 le principe de complexité par le bruit ” 原理发展了这一概念，<ref>See [https://www.google.com/search?&tbm=bks&q=inauthor:%22Henri+Atlan%22%22complexity+from+noise%22 occurrences] on Google Books.</ref><ref>{{cite book |editor-last=François |editor-first=Charles |editor-link= |title=International Encyclopedia of Systems and Cybernetics |year=2011 |origyear=[https://books.google.com/books?id=SZxnQgAACAAJ 1997] |edition=2nd |publisher=Walter de Gruyter |location=Berlin |page=[https://books.google.com/?id=XCn2mn98uEAC&pg=PA107&dq=%22complexity+from+noise+principle%22+Atlan+1972 107] |isbn=978-3-1109-6801-9 |title-link= }}</ref> 该原理首见于1972年出版的《L'organisation biologique et lathéoriede l'information》，<ref>[https://www.google.com/search?&q=%22complexité+par+le+bruit%22%22L'Organisation+biologique+et+la+théorie+de+l'information%22+1972].</ref> 然后是1979年出版的《Entre le cristal et lafumée》。<ref>Nicolis, G. and Prigogine, I. (1977). ''Self-organization in nonequilibrium systems: From dissipative structures to order through fluctuations''. Wiley, New York.</ref> 热力学家伊利亚·[[普利高津]] Ilya Prigogine 提出了类似的原则，即“波动带来有序 Order through fluctuations ”<ref>Nicolis, G. and Prigogine, I. (1977). ''Self-organization in nonequilibrium systems: From dissipative structures to order through fluctuations''. Wiley, New York.</ref> 或“混乱带来有序 Order out of chaos ”<ref>Prigogine, I. and Stengers, I. (1984). ''Order out of chaos: Man's new dialogue with nature''. Bantam Books.</ref>。它也应用在用于解决问题和机器学习的[[模拟退火]]方法中。<ref>{{cite journal |last1=Ahmed |first1=Furqan |title=Simulated annealing variants for self-organized resource allocation in small cell networks |journal=Applied Soft Computing |last2=Tirkkonen |first2=Olav |date=January 2016 |volume=38|pages=762–70 |doi=10.1016/j.asoc.2015.10.028 }}</ref><br /> <br /> ==历史演变==<br /> 系统动力演化可以自动形成组织的想法历史悠久。像德谟克里特 Democritus 和卢克雷修斯 Lucretius 之类的古代[https://en.wikipedia.org/wiki/Atomism 原子论者]认为，一种有计划的智能对于在自然界中创造有序是不必要的，他们认为，只要有足够的时间、空间和物质，有序就会自动产生。<ref>{{cite book |last1 =Palmer |first1= Ada |author-link1= Ada Palmer |title= Reading Lucretius in the Renaissance |date= October 2014|publisher= Harvard University Press |isbn= 978-0-674-72557-7|quote= Ada Palmer explores how Renaissance readers, such as Machiavelli, Pomponio Leto, and Montaigne, actually ingested and disseminated Lucretius, ... and shows how ideas of emergent order and natural selection, so critical to our current thinking, became embedded in Europe’s intellectual landscape before the seventeenth century. |url= http://www.hup.harvard.edu/catalog.php?isbn=9780674725577}}</ref><br /> <br /> <br /> 哲学家勒内·笛卡尔 René Descartes 在其1637年《方法论》的第五部分中假设性提出了'''自组织 Selft-organization '''的概念。他在未发表的作品《世界》中详细阐述了这个想法。<br /> <br /> <br /> 依曼纽尔·康德 Immanuel Kant 在他的1790年《审判批判》中使用了'''“自组织化 Selft-onganizing”'''一词，他认为只有存在这样的实体——其各个部分或“器官 Organs ”同时是终点和手段时——才是有意义的概念。这样的器官系统一定能够像拥有自己的思想一样行事，也就是说，它能够自我支配。<ref name="Kant">{{cite book|title= German Aesthetic|url= https://books.google.com/books?id=eC88AAAAIAAJ&pg=PA64|publisher= CUP Archive|pages= 64–|id= GGKEY:TFTHBB91ZH2}}</ref><br /> <br /> <br /> ''“在这样的天然产物中，其每一个部件都因其他剩余部件的存在而存在，也可以说它的存在是为了其他部件和整个整体，这是作为一种手段，或器官……该部件必须是可以产生其他部件的器官——因此每个部件都会相互产生其他部件……只有在这些条件和关系下，这样的产物才能成为一个系统的和自组织的存在，而且因此才能被称为一个物理结束。”''<ref name=Kant/><br /> <br /> <br /> 萨迪·卡诺 Sadi Carnot，1796-1832 和鲁道夫·克劳修斯 Rudolf Clausius，1822-1888 在19世纪发现了热力学第二定律。它指出：总的熵，有时被理解为无序，在一个孤立的系统中总会随着时间而增加。这意味着，如果没有外部联系降低系统中其他部位的'''有序 Order ''' 例如，通过消耗电池的低熵能量来扩散高熵热，那么系统无法自发地增加'''有序。<ref>Nicolas Léonard Sadi Carnot|Carnot, S. (1824/1986). [http://www.worldcat.org/title/reflections-on-the-motive-power-of-fire-a-critical-edition-with-the-surviving-scientific-manuscripts-translated-and-edited-by-fox-robert/oclc/812944517&referer=brief_results ''Reflections on the motive power of fire''], Manchester University Press, Manchester UK</ref><ref>{{cite journal |last= Clausius |first= R. |author1-link= |title= Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten Lassen |journal= Annalen der Physik |year= 1850|volume= 79 |issue= 4 |pages= 368–97, 500–24 |url= http://gallica.bnf.fr/ark:/12148/bpt6k15164w/f518.image |doi= 10.1002/andp.18501550403 |bibcode = 1850AnP...155..500C |hdl= 2027/uc1.$b242250 |hdl-access= free }} Translated into English: {{cite journal|last= Clausius |first= R. |title= On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom|journal= London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |date= July 1851 |volume= 2 |series= 4th |issue= VIII |pages= 1–21, 102–19 |url= https://archive.org/stream/londonedinburghd02lond#page/1/mode/1up|accessdate= 26 June 2012|doi= 10.1080/14786445108646819 }}</ref><br /> <br /> <br /> 18世纪的思想家试图理解“形式的普遍定律 Universal laws of form ”，以解释观察到的生物体形式。这个想法与'''拉马克主义 Lamarckism '''联系在一起，并声名狼藉，直到20世纪初 D'Arcy Wentworth Thompson 1860–1948 试图复兴它。<ref name="Ruse">{{cite book |author1= Ruse, Michael |editor1-last= Henning |editor1-first= Brian G. |editor2-last= Scarfe |editor2-first= Adam |title= Beyond Mechanism: Putting Life Back Into Biology |date= 2013 |publisher= Lexington Books |page= 419 |url= https://books.google.com/books?id=3VtosxAtq-EC|chapter= 17. From Organicism to Mechanism-and Halfway Back?|isbn= 9780739174371 }}</ref><br /> <br /> <br /> 精神病学家和工程师 Ashby 于1947年向当代科学引入了'''“自组织 Self-organizing”'''一词。<ref name=ashby1947/> 控制论学者 Heinz von Foerster，戈登·帕斯克 Gordon Pask ，斯塔福德·比尔 Stafford Beer 采纳了这一概念，Heinz von Foerster于1960年6月在伊利诺伊大学阿勒顿公园组织了一次有关“自组织原理 The Principles of Self-Organization ”的会议，该会议引发了一系列关于自组织系统的会议。<ref>Asaro, P. (2007). [http://peterasaro.org/writing/Asaro%20HVF%26BCL.pdf "Heinz von Foerster and the Bio-Computing Movements of the 1960s"] in Albert Müller and Karl H. Müller (eds.) ''An Unfinished Revolution? Heinz von Foerster and the Biological Computer Laboratory'' BCL 1958–1976. Vienna, Austria: Edition Echoraum.</ref> 诺伯特·维纳 Norbert Wiener在他的《控制论》第二版中提出了这个想法：《动物与机器中的控制与通讯》 1961 。<br /> <br /> <br /> '''自组织 Self-organization '''与60年代的一般系统理论相关，但是直到物理学家 Hermann Haken等人和复杂系统的研究者从更大范围采纳了这一概念才在科学文献中变得司空见惯起来，这些范围包括宇宙学家埃里希•詹茨 Erich Jantsch ，耗散系统的化学，具备系统思维兴起于1980年代圣塔菲学院 Santa Fe Institute和1990年代复杂适应系统的'''自创生 Autopoiesis '''机制的生物学和社会学领域，以及如今受'''根茎网络理论 Rhizomatic network theory '''深刻影响而出现的颠覆性技术。<ref><br /> As an indication of the increasing importance of this concept, when queried with the keyword <tt>self-organ*</tt>, ''Dissertation Abstracts'' finds nothing before 1954, and only four entries before 1970. There were 17 in the years 1971–1980; 126 in 1981–1990; and 593 in 1991–2000.<br /> </ref><br /> <br /> <br /> 在2008-2009年，'''引导式自组织 Guided self-organization '''的概念开始形成。这种方法旨在针对特定目的调整自组织，以便动态系统可以达到特定的吸引子或结果。这种调整通过限制系统组件之间的局部相互作用，而不是依靠一种明确的控制机制或全局设计蓝图，来限制复杂系统中的自组织过程。通过将任务无关的全局目标与任务相关的对局部相互作用的约束相结合，可以实现预期的结果，例如增加由此带来的内部结构和/或功能。<ref>Phys.org, [https://phys.org/news/2014-02-self-organizing-robots-robotic-crew-foreman.html Self-organizing robots: Robotic construction crew needs no foreman (w/ video)], February 13, 2014.</ref><ref>Science Daily, [https://www.sciencedaily.com/releases/2015/10/151027123342.htm Robotic systems: How sensorimotor intelligence may develop... self-organized behaviors ], October 27, 2015.</ref><br /> <br /> ==按领域==<br /> ===物理===<br /> [[File:ConvectionCells.png|300px|thumb|引力场中的对流单元|right]]<br /> 物理学中的自组织现象包括'''[[相变]] Phase transitions '''和'''自发对称性破缺 Spontaneous symmetry breaking '''，例如'''自发磁化 Spontaneous magnetization ''' ，经典物理学中的晶体生长，激光，<ref>Zeiger, H. J. and Kelley, P. L. (1991) "Lasers", pp. 614–19 in ''The Encyclopedia of Physics'', Second Edition, edited by Lerner, R. and Trigg, G., VCH Publishers.</ref> 超导和量子物理学的'''玻色-爱因斯坦凝聚 Bose–Einstein condensation '''。它在动力学系统，摩擦学，'''自旋泡沫系统 Spin foam systems '''和'''环量子引力 Loop quantum gravity '''<ref>Ansari M. H. (2004) [https://arxiv.org/abs/hep-th/0412307 Self-organized theory in quantum gravity]. arxiv.org</ref> 的'''自组织临界 Self-organized criticality '''中被发现，也在河流盆地和三角洲，'''枝晶凝固 Dendritic solidification （如雪花） '''和'''湍流结构 Turbulent structure '''中被发现。<ref name=":0" /><ref name=":1" /><br /> <br /> <br /> ===化学===<br /> [[File:DNA_nanostructures.png|300px|thumb|左侧示意的DNA结构自组装为右侧的结构|right]]<br /> 化学中的自组织包括分子'''自组装 Molecular self-assembly'''，<ref>{{cite journal|author=Lehn, J.-M. |journal=|title=Perspectives in Supramolecular Chemistry-From Molecular Recognition towards Molecular Information Processing and Self-Organization |volume=27 |issue=11 |year=1988 |pages=89–121 |doi=10.1002/anie.198800891}}</ref> '''反应扩散系统 Reaction–diffusion systems''' 和'''振荡反应 Oscillating reactions'''，<ref>{{cite journal | doi=10.1021/ja01439a007 | year=1921 | author=Bray, William C. | journal=Journal of the American Chemical Society | volume=43 | pages=1262–67 | issue=6 |title=A periodic reaction in homogeneous solution and its relation to catalysis.}}</ref> '''自催化网络 Autocatalytic networks'''，'''液晶 Liquid crystals'''，<ref>{{cite journal |url=http://www.csupomona.edu/~jarego/pubs/RD2_LC.pdf |title=Asymmetric synthesis of a highly soluble 'trimeric' analogue of the chiral nematic liquid crystal twist agent Merck S1011 |last=Rego |first=J.A. |last2=Harvey |first2=Jamie A.A. |last3=MacKinnon |first3=Andrew L. |last4=Gatdula |first4=Elysse |journal=Liquid Crystals |volume=37 |issue=1 |date=January 2010 |pages=37–43 |doi=10.1080/02678290903359291 |url-status=dead |archiveurl=https://www.webcitation.org/5oxBzwQCm?url=http://www.csupomona.edu/~jarego/pubs/RD2_LC.pdf |archivedate=2010-04-13}}</ref> '''网格络合物 Ggrid complexes'''，'''胶质晶体 Colloidal crystals'''，'''自组装单分子层 Self-assembled monolayers'''，<ref>{{cite journal|last1=Love|title= Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology |journal=Chem. Rev. |year=2005 |volume=105 |pages=1103–70 |doi=10.1021/cr0300789 |last2=Estroff |first2=Lara A. |last3=Kriebel |first3=Jennah K.|last4=Nuzzo|first4=Ralph G. |last5=Whitesides |first5=George M. |pmid=15826011 |issue=4 |displayauthors= 1}}</ref><ref name="Raval2003">{{cite journal|last=Barlow |first=S.M.|author2=Raval R.. |title=Complex organic molecules at metal surfaces: bonding, organisation and chirality |journal=Surface Science Report |year=2003 |volume=50 |issue=6–8 |pages=201–341 |doi=10.1016/S0167-5729(03)00015-3 |bibcode=2003SurSR..50..201B }}</ref>'''胶束 Micelles'''，'''嵌段共聚物的微相分离 Microphase separation of block copolymers''' 和'''Langmuir-Blodgett膜 Langmuir–Blodgett films'''。<ref>{{Cite journal | doi=10.1038/srep34095 | title=Large Area Fabrication of Semiconducting Phosphorene by Langmuir-Blodgett Assembly| journal=Sci. Rep.| volume=6| page=34095| year=2016| last1=Ritu | first1=Harneet | pmid=27671093 | pmc=5037434| arxiv=1605.00875| bibcode=2016NatSR...634095K}}</ref><br /> <br /> <br /> ===生物===<br /> [[File:birds.jpg|300px|thumb|鸟类蜂群，生物学中的自我组织的一个例子|right]]<br /> 在生物学中<ref>Camazine, Deneubourg, Franks, Sneyd, Theraulaz, Bonabeau, ''Self-Organization in Biological Systems'', Princeton University|Princeton University Press, 2003.</ref>，从蛋白质和其它生物大分子的'''自发折叠 Spontaneous folding'''，'''磷脂双分子层 Lipid bilayer '''的形成，发育生物学的'''图案形成 Pattern formation'''和'''形态发生 Morphogenesis'''，人体运动的协调，群居昆虫如蜜蜂，蚂蚁，白蚁<ref>{{cite journal|last1=Bonabeau|first1=Eric |display-authors=etal |title=Self-organization in social insects|journal=Trends in Ecology & Evolution|date=May 1997|volume=12|issue=5|pages=188–93|doi=10.1016/S0169-5347(97)01048-3|pmid=21238030 |url=https://dipot.ulb.ac.be/dspace/bitstream/2013/19269/1/020BonabeauTrendsEcologyEvolution97.pdf }}</ref> 和哺乳动物的社会行为，到鸟类和鱼类的'''群集行为 Flocking behaviour'''，都可以观察到自组织现象。<ref>{{cite journal |last1=Couzin |first1=Iain D. |last2=Krause |first2=Jens |title=Self-Organization and Collective Behavior in Vertebrates |journal=Advances in the Study of Behavior |date=2003 |volume=32 |pages=1–75 |url=http://icouzin.princeton.edu/wp-content/uploads/file/PDFs/Couzin%20and%20Krause,%202003.pdf |url-status=dead |archiveurl=https://web.archive.org/web/20161220075600/http://icouzin.princeton.edu/wp-content/uploads/file/PDFs/Couzin%20and%20Krause,%202003.pdf |archivedate=2016-12-20|doi=10.1016/S0065-3454(03)01001-5 |isbn=9780120045327 }}</ref><br /> <br /> <br /> 数学生物学家斯图尔特·考夫曼 Stuart Kauffman 和其他结构主义者认为，自组织可能与自然选择在进化生物学的三个领域中共同发挥作用，即'''种群动力学 Population dynamics'''，'''分子进化 Molecular evolution '''和'''形态发生 Morphogenesis'''。但是，这种假设没有考虑能量在驱动细胞中生化反应中的重要作用。任何细胞中的反应系统都是'''自催化 Self-catalyzing'''的，但不是简单的自组织，因为它们是依赖于持续能量输入的热力学开放系统。<ref>{{cite journal |last1=Fox |first1=Ronald F. |title=Review of Stuart Kauffman, The Origins of Order: Self-Organization and Selection in Evolution |journal=Biophys. J. |date=December 1993 |volume=65 |issue=6 |pages=2698–99 |pmc=1226010 |doi=10.1016/s0006-3495(93)81321-3 |bibcode=1993BpJ....65.2698F}}</ref><ref>{{cite book |author=Goodwin, Brian |authorlink=|title=Beyond the Darwinian Paradigm: Understanding Biological Forms |work=Evolution: The First Four Billion Years |editor1=Ruse, Michael |editor1link=Michael Ruse |editor2=Travis, Joseph |publisher=Harvard University Press |date=2009}}</ref> 自组织不是自然选择的替代方法，但是它限制了进化可以做什么，并提供了诸如膜的自组装之类的机制，以便进化利用这种机制。<ref>{{cite journal |last1=Johnson |first1=Brian R. |last2=Lam |first2=Sheung Kwam |title=Self-organization, Natural Selection, and Evolution: Cellular Hardware and Genetic Software |journal=BioScience |date=2010|volume=60 |issue=11 |pages=879–85 |doi=10.1525/bio.2010.60.11.4 |url=http://bioscience.oxfordjournals.org/content/60/11/879.full}}</ref><br /> <br /> <br /> ===计算机科学===<br /> 来自数学和计算机科学的现象，例如'''[[元胞自动机]] Cellular automata'''，'''[[随机图]] Random graphs'''，以及'''进化计算 Evolutionary computation '''和'''人工生命 Artificial life '''的某些实例，都表现出了自组织的特征。在群体机器人 Swarm robotics 中，自组织被用来产生涌现行为 Emergent behavior。尤其是随机图理论作为复杂系统的一般原理，已被用作自组织的正当理由。在多主体系统领域，理解如何设计一个能够表现出自组织行为的系统是一个活跃的研究领域。<ref>{{cite journal|last1=Serugendo |first1=Giovanna Di Marzo |display-authors=etal |title=Self-organization in multi-agent systems |journal=Knowledge Engineering Review|date=June 2005|volume=20|issue=2|pages=165–89|doi=10.1017/S0269888905000494|url=https://archive-ouverte.unige.ch/unige:120878 }}</ref>优化算法也可以认为是自组织化 Self-organizing的，因为它们旨在找到问题的最优解。如果将这个解视为迭代系统的一个状态，则最优解是系统选定的收敛结构。<ref>{{Cite journal | doi=10.1007/s00521-013-1498-4| title=A framework for self-tuning optimization algorithm| journal=Neural Computing and Applications| volume=23| issue=7–8| pages=2051–57| year=2013| last1=Yang | first1=X. S. | last2=Deb | first2=S. | last3=Loomes | first3=M. | last4=Karamanoglu | first4=M. | arxiv=1312.5667| bibcode=2013arXiv1312.5667Y}}</ref><ref>X. S. Yang (2014) ''Nature-Inspired Optimization Algorithms'', Elsevier.</ref> 自组织网络包括''' [[小世界网络]] Small-world networks '''<ref>{{cite journal|last1=Watts|first1=Duncan J.|last2=Strogatz|first2=Steven H.|title=Collective dynamics of 'small-world' networks|journal=Nature|date=June 1998|volume=393|issue=6684|pages=440–42|doi=10.1038/30918|pmid=9623998|bibcode=1998Natur.393..440W}}</ref> 和''' [[无标度网络]] Scale-free networks'''。它们来自自下而上的相互作用，这与组织内部的自上而下的层次网络不同，后者不是自组织的。<ref name="Clauset">{{Cite journal | doi=10.1137/070710111| last=Clauset| first=Aaron| author2=Cosma Rohilla Shalizi |author3=M. E. J Newman | title=Power-law distributions in empirical data| journal=SIAM Review| year=2009| arxiv=0706.1062 |bibcode=2009SIAMR..51..661C | volume=51 | issue=4| pages=661–703}}</ref> 有人认为云计算系统本质上也是自组织的，<ref>{{Cite journal|last=Zhang, Q., Cheng, L., and Boutaba, R.|date=2010|title=Cloud computing: state-of-the-art and research challenges|journal=Journal of Internet Services and Applications|volume=1|issue=1|pages=7–18|doi=10.1007/s13174-010-0007-6|doi-access=free}}</ref> 但尽管它们具有一定的自治性，它们并不是自我管理的，因为它们的目标不是降低自身的复杂性。<ref>{{Cite arxiv|last1=Marinescu |first1=D. C. |last2=Paya |first2=A. |last3=Morrison |first3=J. P. |last4=Healy |first4=P. |date=2013|title=An auction-driven self-organising cloud delivery model |eprint=1312.2998|class=cs.DC }}</ref><ref>{{Cite journal|last=Lynn |display-authors=etal |date=2016 |title=Cloudlightning: A Framework for a Self-organising and Self-managing Heterogeneous Cloud |url=http://www.scitepress.org/DigitalLibrary/PublicationsDetail.aspx?ID=cHtD7x49Rn8=&t=1 |journal=Proceedings of the 6th International Conference on Cloud Computing and Services Science|page=333 |doi=10.5220/0005921503330338|isbn=978-989-758-182-3|doi-access=free }}</ref><br /> <br /> <br /> ===控制论===<br /> 诺伯特·维纳认为黑盒的'''自动串行识别 Automatic serial identification '''及其随后的'''复制 reproduction '''作为控制论中的自组织。<ref>Wiener, Norbert (1962) "The mathematics of self-organising systems". ''Recent developments in information and decision processes'', Macmillan, N. Y. and Chapter X in ''Cybernetics, or control and communication in the animal and the machine'', The MIT Press.</ref>维纳所称的'''锁相 Phase locking '''或'''“频率吸引 Attraction of frequencies”'''的重要性在他的《控制论——动物与机器中的控制与通信》第二版中进行了讨论。<ref>''Cybernetics, or control and communication in the animal and the machine'', The MIT Press, Cambridge, Massachusetts and Wiley, NY, 1948. 2nd Edition 1962 "Chapter X "Brain Waves and Self-Organizing Systems" pp. 201–02.</ref> 埃里克·德雷克斯勒 K. Eric Drexler 将'''自我复制 Self-replication '''视为纳米和'''通用组装 universal assembly '''的关键步骤。<ref>William Ross Ashby|Ashby, William Ross](1952) ''Design for a Brain'', Chapter 5 Chapman & Hall</ref>相比之下，当 Ross Ashby 的同态调节器——四个同时连通的检流计——受到干扰时，会收敛于许多可能的稳定状态之一。Ross Ashby使用各种状态计数方法来描述稳定状态，并推导出'''“良好调节器 Good Regulator ”''' 定理，<ref>{{cite journal|title=Every good regulator of a system must be a model of that system |author=Conant, R. C.|author2=Ashby, W. R. |journal=Int. J. Systems Sci.|volume=1 |issue=2 |pages=89–97 |year=1970 |url=http://pcp.vub.ac.be/Books/Conant_Ashby.pdf |doi=10.1080/00207727008920220}}</ref> 该定理要求内部模型具有自组织的持久性和稳定性。例如，'''奈奎斯特稳定性标准 Nyquist stability criterion'''。沃伦·麦卡洛克 Warren McCulloch 提出的'''“潜在命令冗余 Redundancy of Potential Command”'''，是大脑和人类神经系统组织的特征，也是自组织的必要条件。Heinz von Foerster提出了'''“冗余度 Redundancy”'''，<math>R=1-H /H_{max}</math>，其中<math>H</math>是熵。<ref>{{cite journal|author=von Foerster, Heinz |author2= Pask, Gordon |title=A Predictive Model for Self-Organizing Systems, Part I|journal=Cybernetica|volume= 3|pages= 258–300|year=1961}}</ref><ref>{{cite journal|author=von Foerster, Heinz |author2= Pask, Gordon |title=A Predictive Model for Self-Organizing Systems, Part II|journal=Cybernetica|volume= 4 |pages=20–55|year= 1961}}</ref> 本质上，这表明未使用的潜在通信带宽是对自组织的一种度量。<br /> <br /> <br /> 1970年代，Stafford Beer 认为自组织对于持久的生命系统的自治是必要的。他将'''活性系统模型 viable system model'''应用于管理。它由五个部分组成：<br /> #监视生存过程的表现<br /> #通过规则的递归应用进行管理<br /> #稳态操作控制<br /> #开发 <br /> #使得在环境干扰下依然可维持身份<br /> <br /> <br /> 通过警报“algedonic loop”反馈来优选焦点：这种反馈是一种对相对于标准功能表现不足或超出表现所产生的疼痛和愉悦的敏感性。<ref>"Brain of the Firm" Alan Lane (1972); see also Viable System Model in "Beyond Dispute", and Stafford Beer (1994) "Redundancy of Potential Command" pp. 157–58.</ref><br /> <br /> <br /> 在1990年代，Gordon Pask 辩称，von Foerster 的H和Hmax不是独立的，而是通过可数的'''无限递归并发自旋过程 Countably infinite recursive concurrent spin processes '''相互作用的，<ref name=p1996/> 他称之为概念。他严格定义了“建立关系的程序 A procedure to bring about a relation”这一概念，<ref name=p1973/> 使得他的定理“相似概念排斥，不同概念吸引 Like concepts repel, unlike concepts attract” ，<ref>{{Cite journal | doi=10.1108/03684920110391913| title=On Gordon Pask| journal=Kybernetes| volume=30| issue=5/6| pages=673–82| year=2001| last1=Green | first1=N. }}</ref> 以得出一种通用的、基于自旋的自组织原理。他的原则是一项排除原则，“ 非二重性 There are No Doppelgangers ”意味着没有两个概念完全相同。经过足够的时间后，所有概念都会吸引并合并成为粉红噪音 Pink noise。<ref>Pask, Gordon (1993) [http://www.cybsoc.org/PasksIAT.PDF ''Interactions of Actors (IA), Theory and Some Applications''].</ref><ref name="p1996">{{cite journal |author=Pask, Gordon |year=1996 |url=http://www.cybsoc.org/GPprog.PDF |title=Heinz von Foerster's Self-Organisation, the Progenitor of Conversation and Interaction Theories |journal= Systems Research |volume=13|issue= 3 |pages=349–62 |doi=10.1002/(sici)1099-1735(199609)13:3<349::aid-sres103>3.3.co;2-7}}</ref>该理论应用于可以产生持久、连贯产品的所有组织封闭 Organizationally closed 或体内平衡 Homeostatic 的过程，这些产品会不断发展，学习和适应。<br /> <br /> <br /> ===人类社会===<br /> [[File:CIA_Map_of_International_illegal_drug_connections.gif|300px|thumb|国际毒品贩卖路线的社会自组织|right]]<br /> 社会动物的自组织行为和简单数学结构的自组织现象，都表明在人类社会中应该存在自组织。自组织的迹象通常是自组织物理系统所体现出的统计属性。社会学，经济学，行为金融学和人类学中存在很多这样的例子，比如'''临界质量 Critical mass'''，'''羊群效应 Herd behaviour'''，'''集体思维 Groupthink '''等。<ref>''[http://cmol.nbi.dk/models/ Interactive models for self organization and biological systems]'' Center for Models of Life, Niels Bohr Institute, Denmark</ref><br /> <br /> <br /> 在社会理论中，尼古拉斯·卢曼 Niklas Luhmann 1984 引入了'''自我指涉 Self-referentiality'''的概念作为自组织理论的社会学应用。对于卢曼而言，社会系统的要素是'''自我再生产 Self-producing '''的交流，即交流产生进一步的交流，因此，只要存在不断变化的交流，社会系统就可以自我复制。对于卢曼而言，人类就是系统环境中的传感器。卢曼通过'''功能分析 Functional analyses '''和系统理论发展出一套关于社会及其子系统的进化论。<ref>Niklas Luhmann|Luhmann, Niklas (1995) ''Social Systems''. Stanford, California: Stanford University Press. </ref><br /> <br /> <br /> 在经济学中，市场经济有时被认为是自组织的。保罗·克鲁格曼 Paul Krugman 在他的著作《自组织经济 The Self Organizing Economy》中阐述了市场自组织在商业周期中的作用。弗里德里希·哈耶克 Friedrich Hayek 创造了术语'''“ 耦合秩序 catallaxy” '''，以描述一种'''“自愿合作的自组织系统 Self-organizing system of voluntary co-operation”''',这与自由市场经济中的自发秩序有关。新古典经济学家认为，加强中央计划通常会使自组织的经济体系效率降低。从另一个角度来看，经济学家认为市场失灵如此明显以至于自组织产生了不良结果，因此国家应指导生产和定价。大多数经济学家都采取中间立场，并建议将市场经济和'''计划经济 Command economy '''的特征混合在一起有时称为'''混合经济 Mixed economy '''。当应用在经济学领域时，自组织的概念很容易变成一种意识形态上的渗透。<ref name="Biel2009">{{Cite journal| author=Biel, R. |author2=Mu-Jeong Kho |url=http://rechercheregulation.files.wordpress.com/2013/01/rr_working_serieid_2009-1.pdf |title=The Issue of Energy within a Dialectical Approach to the Regulationist Problematique |journal=Recherches & Régulation Working Papers, RR Série ID 2009-1 |pages=1–21 |publisher=Association Recherche & Régulation |date=November 2009 |accessdate=2013-11-09}}</ref><ref>Alan Marshall (New Zealand author)|Marshall, A.(2002) ''The Unity of Nature'', Chapter 5. Imperial College Press. </ref><br /> <br /> <br /> ===学习领域===<br /> 使他人“学习如何学习”<ref>Rogers.C. (1969). ''Freedom to Learn''. Merrill</ref> 通常是指教导他们如何服从于被教导。'''自组织学习 Self-organised learning, SOL '''<ref>Thomas L.F. & Augstein E.S. (1985) ''Self-Organised Learning: Foundations of a conversational science for psychology''. Routledge (1st Ed.)</ref><ref>Thomas L.F. & Augstein E.S. (1994) ''Self-Organised Learning: Foundations of a conversational science for psychology''. Routledge (2nd Ed.)</ref><ref>Thomas L.F. & Augstein E.S. (2013) ''[https://books.google.com/books?id=xWVcDQAAQBAJ&printsec=frontcoverSelf-Organised Learning: Foundations of a conversational science for psychology]''. Routledge (Psy. Revivals)</ref> 否认“专家最了解”或存在“最佳方法”，<ref>Harri-Augstein E. S. and Thomas L. F. (1991) ''Learning Conversations: The S-O-L way to personal and organizational growth''. Routledge (1st Ed.)</ref><ref>Harri-Augstein E. S. and Thomas L. F. (2013) ''Learning Conversations: The S-O-L way to personal and organizational growth''. Routledge (2nd Ed.)</ref><ref>Harri-Augstein E. S. and Thomas L. F. (2013)''Learning Conversations: The S-O-L way to personal and organizational growth''. BookBaby (eBook)</ref> 反而坚持认为“个体层面显著的、相关的和可行意义的建构”，<ref>Illich. I. (1971) ''A Celebration of Awareness''. Penguin Books.</ref> 应由学习者进行体验性尝试。<ref>Harri-Augstein E. S. (2000) ''The University of Learning in transformation''</ref> 这可能是协作完成的，而且个人收获更大。<ref>Schumacher, E. F. (1997) ''This I Believe and Other Essays (Resurgence Book)''. </ref><ref>Revans R. W. (1982) ''The Origins and Growth of Action Learning'' Chartwell-Bratt, Bromley</ref> 它被视为一生的过程，并不受限于特定的学习环境家庭，学校，大学，也不受限于父母或教授等权威机构的控制。<ref>Thomas L.F. and Harri-Augstein S. (1993) "On Becoming a Learning Organisation" in ''Report of a 7 year Action Research Project with the Royal Mail Business''. CSHL Monograph</ref> 它需要通过学习者的亲身经历去尝试、并且不断去修正。<ref>Rogers C.R. (1971) ''On Becoming a Person''. Constable, London</ref> 它也不必受限于意识或语言。<ref>Prigogyne I. & Sengers I. (1985) ''Order out of Chaos'' Flamingo Paperbacks. London</ref>弗里特霍夫·卡普拉 Fritjof Capra 声称，这自组织学习，在心理学和教育中鲜为人知。<ref>Capra F (1989) ''Uncommon Wisdom'' Flamingo Paperbacks. London</ref> 它可能与控制论有关，<ref name=p1973>Pask, G. (1973). ''Conversation, Cognition and Learning. A Cybernetic Theory and Methodology''. Elsevier</ref><ref>Bohm D. (1994) ''Thought as a System''. Routledge.</ref>因为它涉及'''负反馈控制回路 Negative feedback control loop。'''它可以作为学习谈话或对话在学习者之间或一个人进行。<ref>Maslow, A. H. (1964). ''Religions, values, and peak-experiences'', Columbus: Ohio State University Press.</ref><ref>''Conversational Science'' Thomas L.F. and Harri-Augstein E.S. (1985)</ref><br /> <br /> <br /> ===交通流===<br /> 交通流中驾驶员的自组织行为几乎决定了交通的所有时空行为，例如高速公路瓶颈处的交通故障，高速公路通行能力以及交通拥堵的出现。在1996–2002年，鲍里斯·克纳 Boris Kerner 的三相交通理论解释了这些复杂的自组织效应。<ref>{{cite journal | last1 = Kerner | first1 = Boris S. | year = 1998 | title = Experimental Features of Self-Organization in Traffic Flow | journal = Physical Review Letters | volume = 81| issue = 17 | pages = 3797–3800| doi=10.1103/physrevlett.81.3797 | bibcode=1998PhRvL..81.3797K}}</ref><br /> <br /> <br /> ===语言学===<br /> 随着个体和群体行为与生物进化相互作用，秩序在语言的进化中自发出现。<ref>{{cite book |last1=De Boer|first1=Bart |title=Self-organization and language evolution |work=The Oxford Handbook of Language Evolution |editor=Gibson, Kathleen R. |editor2=Tallerman, Maggie |date=2011 |publisher=Oxford}}</ref><br /> <br /> <br /> ===研究基金===<br /> 自组织拨款 Self-organized funding allocation，SOFA 是为科学研究分配资金的一种方法。在这个系统中，每个研究人员都被分配了相等数量的资金，并且被要求匿名分配他们一部分资金用于其他人的研究。SOFA的支持者认为，这将导致与目前的拨款系统相似的资金分配，但开销却更少。2016年，SOFA的测试试点在荷兰开始。<ref>{{cite journal |last1=Bollen |first1=Johan |title=Who would you share your funding with? |journal=Nature |date=8 August 2018 |volume=560 |issue=7717 |pages=143 |doi=10.1038/d41586-018-05887-3 |pmid=30089925 |language=EN|bibcode=2018Natur.560..143B |doi-access=free }}</ref> In 2016, a test pilot of SOFA began in the Netherlands.<ref>{{cite web |last1=Coelho |first1=Andre |title=NETHERLANDS: A radical new way do fund science {{!}} BIEN |url=https://basicincome.org/news/2017/05/netherlands-radical-new-way-fund-science/ |accessdate=2 June 2019}}</ref><br /> <br /> ==批判==<br /> 海因茨·佩格尔斯 Heinz Pagels 在1985年对伊利亚·普里戈金 Ilya Prigogine和伊莎贝尔·斯滕格斯 Isabelle Stengers合著的《今日物理学中的秩序与混乱 Order Out of Chaos in Physics Today》一书的评论中呼吁权威：<ref>{{cite journal|url=http://www.fefox.com/ARTICLES/Pagels-PrigogineinPhysicsToday1985.pdf|author=Pagels, H. R. |title=Is the irreversibility we see a fundamental property of nature?|journal=Physics Today|volume=38 |issue=1 |date=January 1, 1985|pages=97–99|doi=10.1063/1.2813716|bibcode=1985PhT....38a..97P}}</ref><br /> <br /> <br /> ''大多数科学家会同意生物物理学家L. a . Blumenfeld在《生物物理学问题》（施普林格 Verlag, 1981）中表达的批判观点，他写道:“有意义的宏观生物结构的排序并不是由于某些参数或系统超过其临界值而产生的。”这些结构是按照类似复杂建筑结构的程序建造的，这些有意义的信息是在数十亿年的化学和生物进化过程中产生的。”生命是微观组织的结果，而不是宏观组织的结果。''<br /> <br /> 当然，Blumenfeld并没有进一步回答那些类似于程序的结构最初是如何出现的问题。他的解释直接导致了无限的倒退。<br /> <br /> <br /> ''简而言之，他们（Prigogine和Stengers）坚持认为，时间不可逆性不是来自于一个与时间无关的微观世界，而是它本身的根本。他们的想法的优点在于，它解决了他们所认为的关于物理中时间本质的“理论冲突”，使得大多数物理学家会同意。但既没有经验证据来支持他们的观点，也没有数学上的必要性，没有所谓的“教义冲突”，只有Prigogine和他的几个同事坚持这些推测。尽管他们作出了努力，这些推测仍然处于科学可信性的边缘地带。''<br /> <br /> <br /> 在神学方面，托马斯·阿奎那 Thomas Aquinas（1225-1274）在他的《神学总论 Summa Theologica》中否定了某物可以成为其自身组织的自给自足原因的观点，从而假定了一个目的性创造的宇宙：<ref>[http://www.newadvent.org/summa/1002.htm#article3 Article 3. Whether God exists?] newadvent.org</ref><br /> <br /> <br /> ''既然自然在一个更高的动因的指导下，为一个特定的目的而工作，那么自然所做的任何事情都必须追溯到上帝，追溯到它的最初的原因。因此，无论自愿做什么，也必须追溯到一些比人类理性或意志更高级的原因，因为这些原因可以改变或失败;因为所有可以改变的、有缺陷的事物都必须追溯到一个不可改变的、自我必须的第一原则，正如文章正文所示。''<br /> <br /> ==参阅==<br /> *[https://en.wikipedia.org/wiki/Autopoiesis 自创生 Autopoiesis]<br /> *[https://en.wikipedia.org/wiki/Autowave 自动波 Autowave]<br /> *[https://en.wikipedia.org/wiki/Self-organized_criticality_control 自组织的临界控制 Self-organized criticality control]<br /> *[https://en.wikipedia.org/wiki/Free_energy_principle 自由能原理 Free energy principle]<br /> *[[信息论 Information theory]]<br /> *[https://en.wikipedia.org/wiki/Adrian_Bejan#Constructal_law 构造法则 Constructal law]<br /> *[https://en.wikipedia.org/wiki/Swarm_intelligence 群体智能 Swarm intelligence]<br /> *蝴蝶效应 Butterfly effect - 集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 (swarma.org)<br /> <br /> ==参考文献==<br /> <references/><br /> <br /> <br /> ==编者推荐==<br /> [[File:3-1534215542.jpeg|300px|thumb|[https://swarma.org/?p=95 《Science Robotics：无人机的自组织飞行和集群智慧》]|right]]<br /> ===集智文章推荐===<br /> ====[https://swarma.org/?p=95 《Science Robotics：无人机的自组织飞行和集群智慧》]====<br /> 超级碗和奥运会开幕式上的无人机表演，都只是人为控制的程序，而在最近一期的 Science 子刊 Science Robitics 上，研究者经过算法优化和参数调节，让无人机群自发形成了非常优美的、自组织的集群行为。<br /> <br /> <br /> ====[https://swarma.org/?p=13286 《自愈路网：城市道路网交通事故的自组织管理策略 | 论文速递10篇》]====<br /> 交通拥堵有没有可能“自行治愈”？答案是肯定的，研究人员提出了一种新颖的自组织交通管理策略，一旦所有受影响的交通流量沿着剩余的道路容量重新分配，交通网络就会“自行治愈”。<br /> <br /> <br /> ====[https://swarma.org/?p=8883 《混合型社会：设计自组织系统集群行为的挑战及前景 | 复杂性文摘》]====<br /> 混合型社会是一种由不同组件组成的自组织的集群系统，这种自组织混合型社会面临哪些挑战？又有怎样的解决思路？<br /> <br /> <br /> ===课程推荐===<br /> ====[https://campus.swarma.org/play/coursedetail?id=10671 《自组织理论》]====<br /> 自组织现象的研究对象主要是复杂的自组织系统（生命系统，社会系统）的形成和发展机制问题，即在一定条件下，系统是如何自动地由无序走向有序，由低级有序走向宏结构和功能自发产生于自然界的许多领域中，我们能否获得统一普适的科学理解？本课程由北京师范大学系统科学学院教授狄增如亲授，帮助梳理了科学的发展脉络，介绍了时间反演对称、热力学第二定律及自组织现象的理论方法。<br /> <br /> <br /> ====[https://campus.swarma.org/play/coursedetail?id=11008 《结构与功能：从无序到有序》]====<br /> 系统科学中，有一条很重要的原理，就是系统结构和系统环境以及它们之间的关联关系，决定了系统整体性和功能。系统整体性与功能是内部系统结构与外部系统环境综合集成的结果，一个复杂系统的涌现特性的例子就是蚂蚁群体。另一个蚂蚁头脑简单，但是整个蚂蚁群体通过自组织而涌现出了高级复杂的蚂蚁社会结构。它们形成了非常明显的社会分工。本课程由北京师范大学系统科学学院教授李红刚亲授，一起探讨系统的结构与功能，聚焦于自组织涌现，如何从无序走向有序。<br /> <br /> <br /> ----<br /> 本中文词条由[[用户:木子二月鸟|木子二月鸟]]、[[用户:乐多多|乐多多]]用户参与编译，[[用户:苏格兰|苏格兰]]用户审校，[[用户:乐多多|乐多多]]编辑欢迎在讨论页面留言。<br /> <br /> <br /> '''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''<br /> [[Category:控制论]]<br /> [[Category:系统科学]]<br /> [[Category:自组织]]<br /> [[Category:物理概念]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E9%A1%B6%E7%82%B9&diff=33923 顶点 2023-01-16T13:00:08Z

<p>TYcl20：/* 参考文献 */</p> <hr /> <div>{{#seo:<br /> |keywords=图论,顶点<br /> |description=图论，顶点<br /> }}<br /> [[Image:6n-graf.svg.png|thumb|一个具有6个顶点和7条边的图，其中最左边数字6的顶点是'''<font color="#ff8000"> 叶顶点 Leaf Vertex</font>'''或叫做'''<font color="#ff8000"> 悬挂点 Pendant Vertex</font>''']]<br /> <br /> 在数学上，更具体地说在[[图论]]中，图这一抽象对象的基本组成单元是顶点或节点：[[无向图]]由一组顶点和一组边（每条边由一对顶点组成，不区分这俩顶点的顺序）组成，而[[有向图]]由一组顶点和一组弧（每条弧由一对顶点组成，区分这俩顶点的顺序）组成。在抽象图的图示中，一般而言，带标注的圆圈表示顶点，两个顶点之间的直线或箭头表示边。直线用于表示无向图的边，箭头表示有向图的边。<br /> <br /> 从图论的观点来看，顶点被视为没有属性且不可分割的对象。无论这些顶点所组成的图来自什么样的应用场景，无论在这些应用场景中，顶点所表示的对象又有什么额外的结构。例如: 计算机科学领域中的语义网络，就可以抽象为图，其顶点表示概念或对象的类。<br /> <br /> <br /> 若图包含由顶点<math>v</math>和<math>w</math>组成的边<math>(v,w)</math>，则称顶点<math>w</math><font color="#ff8000">'''邻接于adjacent to'''</font>顶点<math>v</math>;由所有邻接于<math>v</math>的顶点而组成的图，被称为这些顶点的导出<font color="#ff8000">'''子图induced subgraph'''</font>，它也被称为顶点<math>v</math>的<font color="#ff8000">'''邻域 neighborhood'''</font>。<br /> <br /> </br></br><br /> <br /> ==顶点类型==<br /> <br /> [[File:Small Network.png|alt=A small example network with 8 vertices and 10 edges.|thumb|用具有8个顶点(其中一个是孤立的)和10条边的网络示意。]]<br /> <br /> <br /> 在抽象图中，顶点<math>v</math>的[[度 degree]]，记作<math>𝛿(v)</math>，是所有关联于<math>v</math>的边的数量。度为0的顶点被称作'''孤立顶点 isolated vertex'''，这样的顶点不是任何边的端点(如图2所示，这一抽象图中含有一个孤立顶点)<ref>[[:File:Small Network.png]]; example image of a network with 8 vertices and 10 edges</ref><br /> <br /> 度为1的顶点被称为'''叶顶点 leaf vertex'''，也称<font color="#ff8000">'''叶子顶点、叶节点、悬挂顶点 pendant vertex'''</font>。<br /> <br /> <br /> 在有向图中，我们可以根据边的方向，把顶点的度分为出度 outdegree(也称出次数)，记作<math>𝛿^+(v)</math>和入度 indegree(也称入次数)，记作<math>𝛿^−(v)</math>。一个顶点的出度指的是，所有从这个顶点出发，连接其他顶点的箭头的数量。与此相反，一个顶点的入度指的是，所有从其他顶点出发，连接到这个顶点的箭头的数量。在有向图中，有可能出现两种顶点：源顶点 source vertex 和汇顶点 sink vertex。前者指入度为0的顶点，后者指出度为0的顶点。<br /> <br /> <br /> 若一个顶点的邻域恰好能构成[[团 clique]]，即这个顶点邻域中的任意两个顶点都是相邻的，那么这个顶点被称为'''单纯形顶点 simplicial vertex'''，也译为单纯顶点。与所有其他顶点相邻的顶点，被称为'''泛顶点 universal vertex'''。<br /> <br /> <br /> 若移除某一顶点(和所有以这个顶点为端点的边)后，图被分离为若干个彼此互不相连的子图，那么这一顶点就被称为'''割顶点 cut vertex''';由割顶点构成的集合被称为顶点分离集。若一个连通图被移除少于<math>k</math>个顶点后，总能保持连通，那么这个图被称为<math>k-顶点连通图</math>。由两两不相邻的顶点所构成的集合，被称为独立集。由图中每条边的一个或两个端点所构成的集合，被称为顶点覆盖。图的顶点空间是向量空间，它的基向量与图的顶点相对应。<br /> <br /> <br /> <br /> 如果一个图具有将任何顶点映射到任何其他顶点的对称性，则该图是'''<font color="#ff8000">顶点传递</font>'''的。<br /> <br /> 如果一个图上存在某种<font color="#ff8000">自同构映射automorphism</font> <math>f: \mathbb{V} \rightarrow V</math>，能把图中任意一个顶点<math>v</math>映射为图中的某个其他顶点<math>u</math> ，同时保持边不变，即若顶点<math>v_1,v_2</math>相邻，那么顶点<math>f(v_1)=u_1</math>和<math>f(v_2)=u_2</math>也相邻，那么我们认为这个图是顶点传递的，这样的图具有某种相应的对称性质。<br /> <br /> <br /> 在<font color="32cd32">图计数</font>和'''<font color="#ff8000">图同构</font>'''的语境下，要注意区分'''有标注的顶点'''和'''无标注的顶点'''。有标注的顶点被关联了额外的信息，以区分这个顶点和其他有标注的顶点;这样一来，只有两个图顶点之间的对应关系是把具有相同标注的顶点配对起来，才能称这两个图是同构的。无标注的顶点，就是只能由其相邻关系而被区分的顶点。<br /> <br /> 在图计数或者图同构的语境中，若图中的顶点都是无标注的顶点，则可以不用考虑上面那样额外信息的影响。只要两个图之间存在顶点之间的映射<math>f: \mathbb{V} \rightarrow W</math>，使得原来连通的顶点，在映射之后依然连通，就可以说这两个图是同构的。<br /> <br /> <br /> 图的顶点类似于但不等同于(高维)多面体的顶点。但多面体的顶点有额外的结构(几何位置)，在图论中未能被假定存在。换句话说，作为概念，图的顶点比多面体的顶点，要更抽象。多面体的骨架构成一个图，其顶点是多面体的顶点，但多面体的顶点有无法在图论中假定存在的其他结构(几何位置) 。多面体中顶点的<font color="32cd32">顶点图形</font>类似于图中顶点的邻域。<br /> <br /> <br><br /> <br /> ==参见==<br /> * [[节点 (计算机科学)]]<br /> <br /> * [[图论]]<br /> <br /> * [[图论术语]]<br /> <br /> <br><br /> ==参考文献==<br /> <br /> {{reflist}}<br /> * Claude Berge|Berge, Claude, ''Théorie des graphes et ses applications''. Collection Universitaire de Mathématiques, II Dunod, Paris 1958, viii+277 pp. (English edition, Wiley 1961; Methuen & Co, New York 1962; Russian, Moscow 1961; Spanish, Mexico 1962; Roumanian, Bucharest 1969; Chinese, Shanghai 1963; Second printing of the 1962 first English edition. Dover, New York 2001)<br /> <br /> * {{Cite book | last=Chartrand | first=Gary | Gary Chartrand | title=Introductory graph theory | date=1985 | publisher=Dover | location=New York | isbn=0-486-24775-9 | pages= | url-access=registration | url=https://archive.org/details/introductorygrap0000char }}<br /> <br /> * {{Cite book |author1=Biggs, Norman |author2=Lloyd, E. H. |author3=Wilson, Robin J. | title=Graph theory, 1736-1936 | date=1986 | publisher=Clarendon Press | location=Oxford [Oxfordshire] | isbn=0-19-853916-9 | pages=|title-link=Graph Theory, 1736–1936}}<br /> <br /> * {{Cite book | last=Harary | first=Frank | Frank Harary | title=Graph theory | date=1969 | publisher=Addison-Wesley Publishing | location=Reading, Mass. | isbn=0-201-41033-8 | pages=}}<br /> <br /> * {{Cite book |author1=Harary, Frank |author2=Palmer, Edgar M. | title=Graphical enumeration | date=1973 | publisher=New York, Academic Press | location= | isbn=0-12-324245-2 | pages=}}<br /> * Dulce I. Valdivia， Manuela Geiß, Maribel Hern´andez Rosales, Peter F. Stadler, and Marc Hellmuth. (2020). ''Hierarchical and Modularly-Minimal Vertex Colorings.'' arXiv.<br /> </br></br><br /> <br /> ==编辑推荐==<br /> [[File:顶点.png|400px}right|thumb|[https://campus.swarma.org/course/1754 巴拉巴西网络科学系列课程]]]<br /> ===集智课程推荐===<br /> ====[https://campus.swarma.org/course/1745 漫谈图论的起源、发展与应用]====<br /> 本课程中，介绍了图论中的基本概念和网络科学使用的工具，可以帮助认识真实网络的关键性质。<br /> <br /> <br /> <br /> ====[https://campus.swarma.org/course/1790 书籍领读：图论]====<br /> 本课程中，将讲解巴拉巴西网络科学书籍第一章图论。<br /> <br /> <br /> <br /> ----<br /> 本中文词条由[[用户:鲁鱼陶阴|鲁鱼陶阴]] 参与编译，[[用户:1220978308|1220978308]] 审校，[[用户:不是海绵宝宝|不是海绵宝宝]] 编辑，欢迎在讨论页面留言。<br /> <br /> '''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''<br /> [[分类: 图论]]</div>

TYcl20 https://wiki.swarma.org/index.php?title=%E7%94%A8%E6%88%B7:TYcl20&diff=33922 用户:TYcl20 2023-01-16T11:37:27Z

<p>TYcl20：建立内容为“大家好，我是TY，我在正式接触系统科学前就已经在用系统科学原理在指导生活了，我能感知到各种因素涌现出来的可能状…”的新页面</p> <hr /> <div>大家好，我是TY，我在正式接触系统科学前就已经在用系统科学原理在指导生活了，我能感知到各种因素涌现出来的可能状态，也会用蝴蝶效应去判断某个节点会对以后有深远的影响。现在，我开始深入学习系统科学，期望有一天能读上系统科学的研究生，甚至，与集智科学家们交流。</div>

TYcl20