更改

在CCC的情况下，时间序列数据块的复杂性是基于压缩难度（Effort to Compress，ETC）来计算的<ref name=nagaraj_2013>{{cite journal |last1=Nagaraj |first1=Nithin |last2=Balasubramanian |first2=Karthi |last3=Dey |first3=Sutirth |title=A new complexity measure for time series analysis and classification |journal=The European Physical Journal Special Topics |volume=222 |issue=3 - 4 |pages=847 - 860 |year=2013 |url=https://link.springer.com/article/10.1140/epjst/e2013-01888-9}}</ref>。为了将CCC从<math>X</math>估计到<math>Y</math>，我们计算<math>CC(\Delta Y|Y_{past})</math>——时间序列<math>Y</math>的当前数据窗口<math>\Delta Y</math>在其自身过去<math>Y_{past}</math>条件下的动态复杂性，将其与<math>CC(\Delta Y|Y_{past}, X_{past})</math>——<math>\Delta Y</math>在<math>Y</math>和<math>X</math>的过去<math>(Y_{past}, X_{past})</math>共同条件下的动态复杂性进行比较。数学上，

在CCC的情况下，时间序列数据块的复杂性是基于压缩难度（Effort to Compress，ETC）来计算的<ref name=nagaraj_2013>{{cite journal |last1=Nagaraj |first1=Nithin |last2=Balasubramanian |first2=Karthi |last3=Dey |first3=Sutirth |title=A new complexity measure for time series analysis and classification |journal=The European Physical Journal Special Topics |volume=222 |issue=3 - 4 |pages=847 - 860 |year=2013 |url=https://link.springer.com/article/10.1140/epjst/e2013-01888-9}}</ref>。为了将CCC从<math>X</math>估计到<math>Y</math>，我们计算<math>CC(\Delta Y|Y_{past})</math>——时间序列<math>Y</math>的当前数据窗口<math>\Delta Y</math>在其自身过去<math>Y_{past}</math>条件下的动态复杂性，将其与<math>CC(\Delta Y|Y_{past}, X_{past})</math>——<math>\Delta Y</math>在<math>Y</math>和<math>X</math>的过去<math>(Y_{past}, X_{past})</math>共同条件下的动态复杂性进行比较。数学上，

<math>CC(\Delta Y|Y_{past}) = ETC(Y_{past}+\Delta Y)-ETC(Y_{past})</math>（5）

{{NumBlk|:|<math>CC(\Delta Y|Y_{past}) = ETC(Y_{past}+\Delta Y)-ETC(Y_{past})</math>|{{EquationRef|5}}}}

<math>CC(\Delta Y|Y_{past}, X_{past}) = ETC(Y_{past}+\Delta Y, X_{past}+\Delta Y)-ETC(Y_{past}, X_{past})</math>（6）

{{NumBlk|:|<math>CC(\Delta Y|Y_{past}, X_{past}) = ETC(Y_{past}+\Delta Y, X_{past}+\Delta Y)-ETC(Y_{past}, X_{past})</math>|{{EquationRef|6}}}}

<math>CCC_{X_{past} \to \Delta Y}=CC(\Delta Y|Y_{past})-CC(\Delta Y|Y_{past}, X_{past})</math>（7）

{{NumBlk|:|<math>CCC_{X_{past} \to \Delta Y}=CC(\Delta Y|Y_{past})-CC(\Delta Y|Y_{past}, X_{past})</math>|{{EquationRef|7}}}}

在整个时间序列长度上，随着窗口<math>\Delta Y</math>以步长<math>\delta</math>滑动，从<math>Y</math>到<math>X</math>的平均CCC估计为：

在整个时间序列长度上，随着窗口<math>\Delta Y</math>以步长<math>\delta</math>滑动，从<math>Y</math>到<math>X</math>的平均CCC估计为：

<math>CCC_{X \to Y}=\overline{CCC}_{X_{past} \to \Delta Y}=\overline{CC}(\Delta Y|Y_{past})-\overline{CC}(\Delta Y|Y_{past}, X_{past})</math>（8）

{{NumBlk|:|<math>CCC_{X \to Y}=\overline{CCC}_{X_{past} \to \Delta Y}=\overline{CC}(\Delta Y|Y_{past})-\overline{CC}(\Delta Y|Y_{past}, X_{past})</math>|{{EquationRef|8}}}}

== 基于潜在结果的因果效应度量 ==

== 基于潜在结果的因果效应度量 ==