Сравнение методов

	Нелинейный тест причинности по Грейнджеру Хиемстры-Джонса	Сходящееся перекрестное отображение (CCM)
Область	Эконометрика	Причинно-следственный вывод
Семейство	Hypothesis test	Machine learning
Год появления	1994	2012
Автор метода	Craig Hiemstra & Jonathan Jones	George Sugihara et al.
Тип	Nonparametric hypothesis test	Nonlinear time-series causality test
Основополагающий источник	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.
Другие названия	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
Связанные	3	3
Сводка	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.