เปรียบเทียบวิธี

	การจับคู่ไขว้แบบลู่เข้า (Convergent Cross Mapping - CCM)	การทดสอบความเป็นเหตุเป็นผลแบบแกรนเจอร์ (Granger Causality Test)	การวิเคราะห์ปริมาณการเกิดซ้ำ (Recurrence Quantification Analysis - RQA)	เอนโทรปีการถ่ายทอด
สาขาวิชา	การอนุมานเชิงสาเหตุ	เศรษฐมิติ	ระบบเชิงซ้อน	การอนุมานเชิงสาเหตุ
ตระกูล	Machine learning	Regression model	Machine learning	Machine learning
ปีกำเนิด	2012	1969	2007	2000
ผู้ริเริ่ม	George Sugihara et al.	Clive W. J. Granger	Marwan, Romano, Thiel & Kurths	Thomas Schreiber
ประเภท	Nonlinear time-series causality test	Time-series predictive causality test	Nonlinear time-series characterization	Non-parametric information-theoretic measure
แหล่งต้นตำรับ	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.	Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85(2), 461–464.
ชื่อเรียกอื่น	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	Schreiber Information Transfer, Directed Information Flow, Conditional Mutual Information (directed), Transfer Entropisi
ที่เกี่ยวข้อง	3	5	2	3
สรุป	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.	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.