Сравнение на методи

	Байесов тест за причинност на Тода-Ямамото	Тест за причинност на Грейнджър	Тест за причинност на Toda-Yamamoto Granger	Векторна авторегресия (VAR)
Област	Иконометрия	Иконометрия	Иконометрия	Иконометрия
Семейство	Regression model	Regression model	Hypothesis test	Regression model
Година на възникване	1995 (base); Bayesian variant developed post-2000	1969	1995	1980
Създател	Toda & Yamamoto (1995) for the frequentist base; Bayesian extension by subsequent applied econometricians	Clive W. J. Granger	Hiro Toda & Taku Yamamoto	Christopher A. Sims
Тип	Causality test / VAR-based inference	Time-series predictive causality test	Modified Wald test on augmented VAR	Multivariate time-series model
Основополагащ източник	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.	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.
Други названия	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	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi	VAR, VAR model, vector autoregressive model, multivariate autoregression
Свързани	3	5	3	5
Резюме	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.	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.