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Convergent cross mapping (CCM) is a statistical test for a cause-and-effect relationship between two time series variables that, like the Granger causality test, seeks to resolve the problem that correlation does not imply causation.[1][2] While Granger causality is best suited for purely stochastic systems where the influences of the causal variables are separable (independent of each other), CCM is based on the theory of dynamical systems and can be applied to systems where causal variables have synergistic effects. The fundamental idea of this test was first published by Cenys et al. in 1991[3] and used in a series of statistical approaches (see for example [4], [5], [6]). It was then further elaborated in 2012 by the lab of George Sugihara of the Scripps Institution of Oceanography, La Jolla, California, US.[7] （）
5. 收斂交叉映射(convergent cross mapping)
Convergent cross mapping(CCM) is astatistical testfor acause-and-effect relationshipbetween twotime seriesvariablesthat, like theGranger causalitytest, seeks to resolve the problem thatcorrelation does not imply causation.[1][2]While Granger causality is best suited for purelystochasticsystems where the influences of the causal variables are separable (independent of each other), CCM is based on the theory ofdynamical systemsand can be applied to systems where causal variables have synergistic effects. The test was developed in 2012 by the lab ofGeorge Sugiharaof theScripps Institution of Oceanography,La Jolla, California, USA.
Granger Causality是經典方法，在計量經濟學的時間序列分析中有較多的應用。 除此之外，還有Convergent cross mapping (CCM)。Granger因果模型的前提假設是事件是完全隨機的，但現實情況有很多是非線性、動態且非隨機的，Granger模型對這一類狀況不適用。CCM則能適用於這一類場景，在多組時間序列中構建出因果網絡。 感興趣的可以讀一下這篇發表在Science上的文章：