مقایسهٔ روش‌ها

	نگاشت متقاطع همگرا (CCM)	آزمون علیت گرنجر	آنتروپی انتقال
حوزه	استنتاج علّی	اقتصادسنجی	استنتاج علّی
خانواده	Machine learning	Regression model	Machine learning
سال پیدایش	2012	1969	2000
پدیدآور	George Sugihara et al.	Clive W. J. Granger	Thomas Schreiber
نوع	Nonlinear time-series causality test	Time-series predictive causality test	Non-parametric information-theoretic measure
منبع بنیادین	Sugihara, G., et al. (2012). Detecting causality in complex ecosystems. Science, 338(6106), 496–500.	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424-438.	Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85(2), 461–464.
نام‌های دیگر	CCM, Cross-Convergent Mapping, Empirical Dynamic Modelling Causality, Yakınsak Çapraz Haritalama	Granger causality test, Granger non-causality test, predictive causality test, Granger Nedensellik Testi	Schreiber Information Transfer, Directed Information Flow, Conditional Mutual Information (directed), Transfer Entropisi
مرتبط	3	5	3
خلاصه	Convergent Cross Mapping (CCM) is a nonlinear, state-space method for detecting causality between time-series variables embedded in a shared dynamical system. Introduced by George Sugihara and colleagues in their landmark 2012 Science paper, CCM exploits Takens' embedding theorem: if variable X causally influences Y, the historical record of Y contains enough information to recover the states of X. Causality is confirmed when cross-map skill improves—converges—as the time-series library grows longer.	The Granger causality test, introduced by Clive W. J. Granger in 1969, assesses whether the past values of one time series help predict another beyond what the latter's own past already explains. It defines causality in a strictly predictive sense rather than as a structural or physical cause.	Transfer Entropy (TE) is a non-parametric, information-theoretic measure of directed statistical dependence between two time series, introduced by Thomas Schreiber in 2000. Grounded in Shannon entropy, it quantifies how much information the past of one process Y reduces uncertainty about the next state of another process X, beyond what X's own past already provides. Unlike linear correlation or Granger causality, TE captures nonlinear interactions and requires no model assumptions about the underlying dynamics.