Linganisha mbinu

	Kipimo cha Umuhimu cha Granger cha Toda-Yamamoto	Ubora wa Utegemezi wa Viga (VAR)
Nyanja	Ekonometriki	Ekonometriki
Familia	Hypothesis test	Regression model
Mwaka wa asili	1995	1980
Mwanzilishi	Hiro Toda & Taku Yamamoto	Christopher A. Sims
Aina	Modified Wald test on augmented VAR	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	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi	VAR, VAR model, vector autoregressive model, multivariate autoregression
Zinazohusiana	3	5
Muhtasari	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.