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	Robust Granger Causality	Test przyczynowości Granger wg Todę-Yamamotę
Dziedzina	Ekonometria	Ekonometria
Rodzina	Regression model	Hypothesis test
Rok powstania	2006 (robust variant); 1969 (original Granger)	1995
Twórca	Hacker & Hatemi-J (robust bootstrap variant); Granger (original causality concept)	Hiro Toda & Taku Yamamoto
Typ	Hypothesis test	Modified Wald test on augmented VAR
Źródło pierwotne	Hacker, R. S., & Hatemi-J, A. (2006). Tests for causality between integrated variables using asymptotic and bootstrap distributions: Theory and application. Applied Economics, 38(13), 1489–1500.	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1–2), 225–250.
Inne nazwy	bootstrap Granger causality, heteroscedasticity-robust Granger causality, non-asymptotic Granger causality test, RGC	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi
Pokrewne	4	3
Podsumowanie	Robust Granger causality extends the classic Granger causality framework by using bootstrap-based or heteroscedasticity-robust critical values rather than asymptotic chi-squared tables. This makes the test reliable in finite samples and when the data exhibit non-normality, heteroscedasticity, or near-integration, settings where the standard F- or Wald-based test is known to over-reject.	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.