เปรียบเทียบวิธี

	การจับคู่ไขว้แบบลู่เข้า (Convergent Cross Mapping - CCM)	การทดสอบความเป็นเหตุเป็นผลแบบแกรนเจอร์ (Granger Causality Test)	Sample Entropy
สาขาวิชา	การอนุมานเชิงสาเหตุ	เศรษฐมิติ	ระบบเชิงซ้อน
ตระกูล	Machine learning	Regression model	Machine learning
ปีกำเนิด	2012	1969	2000
ผู้ริเริ่ม	George Sugihara et al.	Clive W. J. Granger	Richman & Moorman
ประเภท	Nonlinear time-series causality test	Time-series predictive causality test	Nonlinear entropy 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.	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.
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	SampEn, Sample Entropy (SampEn), Örneklem Entropisi, Nonlinear Complexity Measure
ที่เกี่ยวข้อง	3	5	2
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.	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.