เปรียบเทียบวิธี

	การทดสอบความเป็นเหตุเป็นผลแบบไม่เชิงเส้นของ Hiemstra-Jones	การจับคู่ไขว้แบบลู่เข้า (Convergent Cross Mapping - CCM)
สาขาวิชา	เศรษฐมิติ	การอนุมานเชิงสาเหตุ
ตระกูล	Hypothesis test	Machine learning
ปีกำเนิด	1994	2012
ผู้ริเริ่ม	Craig Hiemstra & Jonathan Jones	George Sugihara et al.
ประเภท	Nonparametric hypothesis test	Nonlinear time-series causality test
แหล่งต้นตำรับ	Hiemstra, C., & Jones, J. D. (1994). Testing for linear and nonlinear Granger causality in the stock price-volume relation. The Journal of Finance, 49(5), 1639–1664.	Sugihara, G., et al. (2012). Detecting causality in complex ecosystems. Science, 338(6106), 496–500.
ชื่อเรียกอื่น	HJ Nonlinear Causality Test, Hiemstra-Jones Test, Nonlinear Granger Causality (Hiemstra-Jones), HJ Nedensellik Testi	CCM, Cross-Convergent Mapping, Empirical Dynamic Modelling Causality, Yakınsak Çapraz Haritalama
ที่เกี่ยวข้อง	3	3
สรุป	The Hiemstra-Jones test, introduced in 1994, is a nonparametric procedure for detecting nonlinear causal relationships between two time series after removing their linear interdependencies. Developed in the context of stock price and trading volume dynamics, it extends the standard linear Granger causality framework by using correlation integral statistics to detect predictability arising from nonlinear mechanisms that linear VAR models cannot capture.	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.