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	Bayesowska próba przyczynowości Toda-Yamamoty	Test przyczynowości Grangera	Autoregresja Wektorowa (VAR)
Dziedzina	Ekonometria	Ekonometria	Ekonometria
Rodzina	Regression model	Regression model	Regression model
Rok powstania	1995 (base); Bayesian variant developed post-2000	1969	1980
Twórca	Toda & Yamamoto (1995) for the frequentist base; Bayesian extension by subsequent applied econometricians	Clive W. J. Granger	Christopher A. Sims
Typ	Causality test / VAR-based inference	Time-series predictive causality test	Multivariate time-series model
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.	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424-438.	Sims, C. A. (1980). Macroeconomics and Reality. Econometrica, 48(1), 1–48.
Inne nazwy	Bayesian TY causality, Bayesian modified Wald causality, Bayesian Granger non-causality in VAR, BTY causality	Granger causality test, Granger non-causality test, predictive causality test, Granger Nedensellik Testi	VAR, VAR model, vector autoregressive model, multivariate autoregression
Pokrewne	3	5	5
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 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.	Vector Autoregression is a multivariate time-series model in which each variable is regressed on its own lags and the lags of all other variables in the system. Originally proposed by Sims (1980) as a data-driven alternative to large structural macroeconomic models, VAR has become the standard workhorse for dynamic analysis in empirical economics and finance.