Methoden vergleichen

	Bayesian Toda-Yamamoto-Kausalitätstest	Toda-Yamamoto-Granger-Kausalitätstest	Vektorautoregression (VAR)
Fachgebiet	Ökonometrie	Ökonometrie	Ökonometrie
Familie	Regression model	Hypothesis test	Regression model
Entstehungsjahr	1995 (base); Bayesian variant developed post-2000	1995	1980
Urheber	Toda & Yamamoto (1995) for the frequentist base; Bayesian extension by subsequent applied econometricians	Hiro Toda & Taku Yamamoto	Christopher A. Sims
Typ	Causality test / VAR-based inference	Modified Wald test on augmented VAR	Multivariate time-series model
Wegweisende Quelle	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.	Sims, C. A. (1980). Macroeconomics and Reality. Econometrica, 48(1), 1–48.
Aliasnamen	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	VAR, VAR model, vector autoregressive model, multivariate autoregression
Verwandt	3	3	5
Zusammenfassung	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.	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.