مقایسهٔ روش‌ها

	نگاشت متقاطع همگرا (CCM)	آزمون علیت گرنجر	تحلیل کمی بازگشت (RQA)
حوزه	استنتاج علّی	اقتصادسنجی	سیستم‌های پیچیده
خانواده	Machine learning	Regression model	Machine learning
سال پیدایش	2012	1969	2007
پدیدآور	George Sugihara et al.	Clive W. J. Granger	Marwan, Romano, Thiel & Kurths
نوع	Nonlinear time-series causality test	Time-series predictive causality test	Nonlinear time-series characterization
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.	Marwan, N., Romano, M. C., Thiel, M., & Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438(5–6), 237–329.
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	RQA, Recurrence Plot Analysis, Nonlinear Recurrence Analysis, Tekrarlama Kantifikasyon Analizi
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.	Recurrence Quantification Analysis (RQA) is a nonlinear method for characterizing the dynamics of a time series by quantifying the small-scale structure of its recurrence plot. Introduced in its modern, comprehensive form by Marwan, Romano, Thiel, and Kurths in 2007, RQA extracts scalar measures — such as recurrence rate, determinism, laminarity, and Shannon entropy — that capture periodicity, chaos, stationarity, and transitions in complex dynamical systems.