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	Bayesowska próba przyczynowości Toda-Yamamoty	Test przyczynowości Granger wg Todę-Yamamotę
Dziedzina	Ekonometria	Ekonometria
Rodzina	Regression model	Hypothesis test
Rok powstania	1995 (base); Bayesian variant developed post-2000	1995
Twórca	Toda & Yamamoto (1995) for the frequentist base; Bayesian extension by subsequent applied econometricians	Hiro Toda & Taku Yamamoto
Typ	Causality test / VAR-based inference	Modified Wald test on augmented VAR
Źródło pierwotne	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1-2), 225-250.	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	Bayesian TY causality, Bayesian modified Wald causality, Bayesian Granger non-causality in VAR, BTY causality	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi
Pokrewne	3	3
Podsumowanie	The Bayesian Toda-Yamamoto causality procedure combines the Toda-Yamamoto VAR augmentation strategy — which sidesteps the need for pre-testing integration and cointegration — with Bayesian prior-posterior updating. It tests Granger non-causality between time series that may be integrated or cointegrated without requiring differencing or error-correction modeling, while incorporating prior information and producing full posterior distributions over the causal parameters.	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.