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第152行： − + − Tools for investigating time-series data include:+ − + − Tools for investigating time-series data include:+ − + − = = = 调查时间序列数据的工具包括: − − * Consideration of the [[autocorrelation|autocorrelation function]] and the [[Spectral density|spectral density function]] (also [[cross-correlation function]]s and cross-spectral density functions) − * [[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> − * Performing a [[Fourier transform]] to investigate the series in the [[frequency domain]] − * Use of a [[digital filter|filter]] to remove unwanted [[noise (physics)|noise]] − * [[Principal component analysis]] (or [[empirical orthogonal function]] analysis) − * [[Singular spectrum analysis]] − * "Structural" models: − ** General [[State Space Model]]s − ** Unobserved Components Models − * [[Machine Learning]] − ** [[Artificial neural network]]s − ** [[Support vector machine]] − ** [[Fuzzy logic]] − ** [[Gaussian process]] − ** [[Genetic Programming]] − ** [[Gene expression programming]] − ** [[Hidden Markov model]] − ** [[Multi expression programming]] − * [[Queueing theory]] analysis − * [[Control chart]] − ** [[Shewhart individuals control chart]] − ** [[CUSUM]] chart − ** [[EWMA chart]] − * [[Detrended fluctuation analysis]] − * [[Nonlinear mixed-effects model|Nonlinear mixed-effects modeling]] − * [[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> − * [[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> − * [[Dynamic Bayesian network]] − * [[Time-frequency representation|Time-frequency analysis techniques:]] − ** [[Fast Fourier transform]] − ** [[Continuous wavelet transform]] − ** [[Short-time Fourier transform]] − ** [[Chirplet transform]] − ** [[Fractional Fourier transform]] − * [[Chaos theory|Chaotic analysis]] − ** [[Correlation dimension]] − ** [[Recurrence plot]]s − ** [[Recurrence quantification analysis]] − ** [[Lyapunov exponent]]s − ** [[Entropy encoding]] − − * Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions) − * Scaled cross- and auto-correlation functions to remove contributions of slow components − * Performing a Fourier transform to investigate the series in the frequency domain − * Use of a filter to remove unwanted noise − * Principal component analysis (or empirical orthogonal function analysis) − * Singular spectrum analysis − * "Structural" models: − ** General State Space Models − ** Unobserved Components Models − * Machine Learning − ** Artificial neural networks − ** Support vector machine − ** Fuzzy logic − ** Gaussian process − ** Genetic Programming − ** Gene expression programming − ** Hidden Markov model − ** Multi expression programming − * Queueing theory analysis − * Control chart − ** Shewhart individuals control chart − ** CUSUM chart − ** EWMA chart − * Detrended fluctuation analysis − * Nonlinear mixed-effects modeling − * Dynamic time warping − * Cross-correlation − * Dynamic Bayesian network − * Time-frequency analysis techniques: − ** Fast Fourier transform − ** Continuous wavelet transform − ** Short-time Fourier transform − ** Chirplet transform − ** Fractional Fourier transform − * Chaotic analysis − ** Correlation dimension − ** Recurrence plots − ** Recurrence quantification analysis − ** Lyapunov exponents − ** Entropy encoding − − − − − − * 使用 第434行：
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第376行： − + − 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>+ − − Time series metrics or features that can be used for time series classification or regression analysis: − − = = = = 可用于时间序列分类或回归分析的时间序列度量或特征: − − * '''Univariate linear measures''' − ** [[Moment (mathematics)]] − ** [[Spectral band power]] − ** [[Spectral edge frequency]] − ** Accumulated [[Energy (signal processing)]] − ** Characteristics of the [[autocorrelation]] function − ** [[Hjorth parameters]] − ** [[Fast Fourier transform|FFT]] parameters − ** [[Autoregressive model]] parameters − ** [[Mann–Kendall test]] − * '''Univariate non-linear measures''' − ** Measures based on the [[correlation]] sum − ** [[Correlation dimension]] − ** [[Correlation integral]] − ** [[Correlation density]] − ** [[Correlation entropy]] − ** [[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> − ** [[Sample entropy]] − ** {{iw2|Fourier entropy||uk|Ентропія Фур'є}} − ** Wavelet entropy − ** Dispersion entropy − ** Fluctuation dispersion entropy − ** [[Rényi entropy]] − ** Higher-order methods − ** [[Marginal predictability]] − ** [[Dynamical similarity]] index − ** [[State space]] dissimilarity measures − ** [[Lyapunov exponent]] − ** Permutation methods − ** [[Local flow]] − * '''Other univariate measures''' − ** [[Algorithmic information theory|Algorithmic complexity]] − ** [[Kolmogorov complexity]] estimates − ** [[Hidden Markov Model]] states − ** [[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> − ** Surrogate time series and surrogate correction − ** Loss of recurrence (degree of non-stationarity) − * '''Bivariate linear measures''' − ** Maximum linear [[cross-correlation]] − ** Linear [[Coherence (signal processing)]] − * '''Bivariate non-linear measures''' − ** Non-linear interdependence − ** Dynamical Entrainment (physics) − ** Measures for [[Phase synchronization]] − ** Measures for [[Phase locking]] − * '''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> − ** [[Cross-correlation]] − ** [[Dynamic Time Warping]]<ref name="Sakoe 1978"/> − ** [[Hidden Markov Models]] − ** [[Edit distance]] − ** [[Total correlation]] − ** [[Newey–West estimator]] − ** [[Prais–Winsten estimation|Prais–Winsten transformation]] − ** Data as Vectors in a Metrizable Space − *** [[Minkowski distance]] − *** [[Mahalanobis distance]] − ** Data as time series with envelopes − *** Global [[standard deviation]] − *** Local [[standard deviation]] − *** Windowed [[standard deviation]] − ** Data interpreted as stochastic series − *** [[Pearson product-moment correlation coefficient]] − *** [[Spearman's rank correlation coefficient]] − ** Data interpreted as a [[probability distribution]] function − *** [[Kolmogorov–Smirnov test]] − *** [[Cramér–von Mises criterion]] − − * Univariate linear measures − ** Moment (mathematics) − ** Spectral band power − ** Spectral edge frequency − ** Accumulated Energy (signal processing) − ** Characteristics of the autocorrelation function − ** Hjorth parameters − ** FFT parameters − ** Autoregressive model parameters − ** Mann–Kendall test − * Univariate non-linear measures − ** Measures based on the correlation sum − ** Correlation dimension − ** Correlation integral − ** Correlation density − ** Correlation entropy − ** Approximate entropy − ** Sample entropy − ** − ** Wavelet entropy − ** Dispersion entropy − ** Fluctuation dispersion entropy − ** Rényi entropy − ** Higher-order methods − ** Marginal predictability − ** Dynamical similarity index − ** State space dissimilarity measures − ** Lyapunov exponent − ** Permutation methods − ** Local flow − * Other univariate measures − ** Algorithmic complexity − ** Kolmogorov complexity estimates − ** Hidden Markov Model states − ** Rough path signature[1] Chevyrev, I., Kormilitzin, A. (2016) "A Primer on the Signature Method in Machine Learning, arXiv:1603.03788v1" − ** Surrogate time series and surrogate correction − ** Loss of recurrence (degree of non-stationarity) − * Bivariate linear measures − ** Maximum linear cross-correlation − ** Linear Coherence (signal processing) − * Bivariate non-linear measures − ** Non-linear interdependence − ** Dynamical Entrainment (physics) − ** Measures for Phase synchronization − ** Measures for Phase locking − * Similarity measures: − ** Cross-correlation − ** Dynamic Time Warping − ** Hidden Markov Models − ** Edit distance − ** Total correlation − ** Newey–West estimator − ** Prais–Winsten transformation − ** Data as Vectors in a Metrizable Space − *** Minkowski distance − *** Mahalanobis distance − ** Data as time series with envelopes − *** Global standard deviation − *** Local standard deviation − *** Windowed standard deviation − ** Data interpreted as stochastic series − *** Pearson product-moment correlation coefficient − *** Spearman's rank correlation coefficient − ** Data interpreted as a probability distribution function − *** Kolmogorov–Smirnov test − *** Cramér–von Mises criterion − − − − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − * 数据作为时间序列与信封 第693行：
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第495行： − 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> − 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)
无编辑摘要
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
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
===Tools===
===形成，分析时间序列数据的工具与方法===
形成，分析时间序列数据的工具与方法包括:
* 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)
* 调整互相关函数和自相关函数以去除慢分量的贡献
* 在频域中执行一个傅里叶变换来调查这个序列
* 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)
* 调整互相关函数和自相关函数以去除慢分量的贡献
* 在频域中执行一个傅里叶变换来调查这个序列
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*CUSUM 图
*CUSUM 图
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* EWMA 图
* EWMA 图
* 非趋势波动分析
* 非趋势波动分析
* 非线性混合效应建模
* 非线性混合效应建模
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* 动态时间规整互相关
* 动态时间规整互相关
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* 动态贝氏网路
* 动态贝氏网路
* 时频分析技术:
* 时频分析技术:
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* 快速傅里叶变换连续小波转换
* 快速傅里叶变换连续小波转换
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* 短时距傅里叶变换
* 短时距傅里叶变换
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* 混沌分析
* 混沌分析
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* 复发图
* 复发图
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* 递归量化分析
* 递归量化分析
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* Lyapunov 指数
* Lyapunov 指数
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===Measures===
===时间序列量化分析的指标与准则===
* 单变量线性测量
* 单变量线性测量
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* 矩(数学)
* 矩(数学)
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* 谱带功率
* 谱带功率
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* 谱边缘频率
* 谱边缘频率
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* 累积能量(信号处理)
* 累积能量(信号处理)
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* 自相关函数特性
* 自相关函数特性
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* Hjorth 参数
* Hjorth 参数
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* FFT 参数
* FFT 参数
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* 自回归模型参数
* 自回归模型参数
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* 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
* 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
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* 本地流
* 本地流
* 其他单变量度量
* 其他单变量度量
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* 算法复杂度
* 算法复杂度
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* 柯氏复杂性估计
* 柯氏复杂性估计
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* 隐马尔可夫模型状态
* 隐马尔可夫模型状态
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* 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”
* 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”
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* 替代时间序列和替代校正
* 替代时间序列和替代校正
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* 递归损失(非平稳度)
* 递归损失(非平稳度)
* 双变量线性度量
* 双变量线性度量
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* 最大线性互相关
* 最大线性互相关
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* 线性相干性(信号处理)
* 线性相干性(信号处理)
* 双变量非线性度量
* 双变量非线性度量
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* 非线性相互依赖
* 非线性相互依赖
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* 动态卷吸(物理学)
* 动态卷吸(物理学)
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* 相位同步的度量
* 相位同步的度量
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* 相位锁定的度量
* 相位锁定的度量
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* 相似度量:
* 相似度量:
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* 互相关
* 互相关
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* 动态时间规整
* 动态时间规整
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* 隐马尔可夫模型
* 隐马尔可夫模型
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* 编辑距离
* 编辑距离
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* 总相关性
* 总相关性
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* Newey-West 估计
* Newey-West 估计
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* Prais-Winsten 变换
* Prais-Winsten 变换
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* 数据作为向量在乌雷松度量化定理
* 数据作为向量在乌雷松度量化定理
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* 明氏距离
* 明氏距离
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* 马氏距离
* 马氏距离
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* 局部标准差标准差
* 局部标准差
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* 窗口标准差
* 窗口标准差
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* 数据解释为随机序列
* 数据解释为随机序列
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* 斯皮尔曼的秩相关系数
* 斯皮尔曼的秩相关系数
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* 数据解释为概率分布函数
* 数据解释为概率分布函数
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* Kolmogorov-Smirnov 检验
* Kolmogorov-Smirnov 检验
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==Visualization==
==Visualization==
= = 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)
= = 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)