مقایسهٔ روش‌ها

	آزمون علیت گرنجر تودا-یاماموتو	مدل خودرگرسیون برداری (VAR)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Hypothesis test	Regression model
سال پیدایش	1995	2005
پدیدآور	Hiro Toda & Taku Yamamoto	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
نوع	Modified Wald test on augmented VAR	Multivariate time-series model
منبع بنیادین	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.
نام‌های دیگر	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
مرتبط	3	4
خلاصه	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).