Порівняння методів

	Тест Ґранджера на причинність	Тест на причинність за Тодою-Ямамото	Модель векторної авторегресії (VAR)
Галузь	Економетрика	Економетрика	Економетрика
Родина	Regression model	Hypothesis test	Regression model
Рік появи	1969	1995	2005
Автор методу	Clive W. J. Granger	Hiro Toda & Taku Yamamoto	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Тип	Time-series predictive causality test	Modified Wald test on augmented VAR	Multivariate time-series model
Основоположне джерело	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424-438.	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1–2), 225–250.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
Інші назви	Granger causality test, Granger non-causality test, predictive causality test, Granger Nedensellik Testi	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Пов'язані	5	3	4
Підсумок	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.	The Toda-Yamamoto (TY) causality test, introduced by Toda and Yamamoto (1995), provides a robust procedure for testing Granger non-causality in vector autoregressive (VAR) models when the variables may be integrated or cointegrated of arbitrary order. By intentionally over-fitting the VAR with extra lags equal to the maximum integration order, the method bypasses the need for pre-testing cointegration and preserves the standard asymptotic chi-squared distribution of the Wald statistic.	Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005).