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	Bayesowska przyczynowość Grangera	Test przyczynowości Todda-Yamamoty
Dziedzina	Ekonometria	Ekonometria
Rodzina	Regression model	Regression model
Rok powstania	1969 (frequentist); 1984 (Bayesian treatment)	1995
Twórca	Clive W. J. Granger (frequentist basis, 1969); Bayesian extension by Geweke (1984) and subsequent literature	Toda, H. Y. and Yamamoto, T.
Typ	Bayesian causal inference test	Causality test
Źródło pierwotne	Geweke, J. (1984). Inference and causality in economic time series models. Handbook of Econometrics, 2, 1101-1144. Elsevier.	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 Granger test, Bayesian predictive causality, BGC, Bayesian causality in mean	Toda-Yamamoto test, TY causality test, modified Wald test for Granger causality, TY-MWALD
Pokrewne	6	5
Podsumowanie	Bayesian Granger causality tests whether past values of one time series carry predictive information about another, framing the hypothesis through Bayesian inference rather than frequentist p-values. It combines a vector autoregressive (VAR) structure with prior distributions over coefficients and evaluates causal claims via posterior probabilities or Bayes factors, providing a probabilistic and nuanced alternative to the classical Granger test.	The Toda-Yamamoto (TY) causality test is a modified Wald procedure for testing Granger causality in vector autoregressions (VARs) estimated in levels, even when variables are nonstationary or cointegrated. By intentionally over-fitting the VAR with extra lags equal to the maximum integration order, it restores the standard chi-squared asymptotic distribution of the Wald statistic without requiring prior unit-root or cointegration pretesting.