Linganisha mbinu

	Kipimo cha Utafiti cha Utafiti cha Bayesian Toda-Yamamoto	Ubora wa Utegemezi wa Viga (VAR)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1995 (base); Bayesian variant developed post-2000	1980
Mwanzilishi	Toda & Yamamoto (1995) for the frequentist base; Bayesian extension by subsequent applied econometricians	Christopher A. Sims
Aina	Causality test / VAR-based inference	Multivariate time-series model
Chanzo asilia	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.
Majina mbadala	Bayesian TY causality, Bayesian modified Wald causality, Bayesian Granger non-causality in VAR, BTY causality	VAR, VAR model, vector autoregressive model, multivariate autoregression
Zinazohusiana	3	5
Muhtasari	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.	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.