مقایسهٔ روش‌ها

	نگاشت متقاطع همگرا (CCM)	آزمون علیت گرنجر	آنتروپی نمونه (Sample Entropy)
حوزه	استنتاج علّی	اقتصادسنجی	سیستم‌های پیچیده
خانواده	Machine learning	Regression model	Machine learning
سال پیدایش	2012	1969	2000
پدیدآور	George Sugihara et al.	Clive W. J. Granger	Richman & Moorman
نوع	Nonlinear time-series causality test	Time-series predictive causality test	Nonlinear entropy 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.	Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology, 278(6), H2039–H2049.
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	SampEn, Sample Entropy (SampEn), Örneklem Entropisi, Nonlinear Complexity Measure
مرتبط	3	5	2
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.	Sample Entropy (SampEn) is a nonlinear measure of the complexity and regularity of a time series. Introduced by Richman and Moorman in 2000 as an improvement over Approximate Entropy (ApEn), it quantifies the likelihood that similar patterns of a given length in the series remain similar when extended by one additional data point. A higher SampEn value indicates greater irregularity and complexity, while a lower value indicates more regularity or self-similarity.