Linganisha mbinu

	Uchanganuzi wa Ugaidi wa Granger wa Vunja Muundo	Kipimo cha Umuhimu cha Granger cha Toda-Yamamoto	Ubora wa Utegemezi wa Viga (VAR)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Hypothesis test	Regression model
Mwaka wa asili	1995-2010	1995	1980
Mwanzilishi	Granger (1969) causality framework extended by Toda & Yamamoto (1995) and Balcilar et al. (2010)	Hiro Toda & Taku Yamamoto	Christopher A. Sims
Aina	Hypothesis test / time-series model	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.	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	break-robust Granger causality, Granger causality under regime change, time-varying Granger causality, structural change Granger test	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi	VAR, VAR model, vector autoregressive model, multivariate autoregression
Zinazohusiana	3	3	5
Muhtasari	Structural break Granger causality extends the classic Granger causality framework to accommodate regime shifts and parameter instability in time series. By detecting break points and testing causality within sub-samples or via rolling/recursive windows, it reveals whether a predictive relationship between variables switches on, switches off, or changes direction over time.	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.