Linganisha mbinu

	Jaribio la Muundo wa Toda-Yamamoto wa Kusababisha	Kipimo cha Utafiti wa Kiasababishi cha Toda-Yamamoto
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1995 (base); structural break extensions widely adopted 2000s–2010s	1995
Mwanzilishi	Toda & Yamamoto (1995); structural break extensions by Zivot & Andrews (1992) and subsequent applied literature	Toda, H. Y. and Yamamoto, T.
Aina	Causality test	Causality test
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.
Majina mbadala	SB-TY causality, structural break modified Wald test causality, Fourier Toda-Yamamoto causality, causality with regime shifts	Toda-Yamamoto test, TY causality test, modified Wald test for Granger causality, TY-MWALD
Zinazohusiana	6	5
Muhtasari	The structural break Toda-Yamamoto causality test extends the standard Toda-Yamamoto modified Wald (MWALD) procedure to accommodate one or more structural breaks in the time series. By identifying break dates first and then including dummy variables in the augmented VAR, the test maintains its valid asymptotic chi-squared distribution regardless of the integration or cointegration order of the variables, even in the presence of regime shifts.	The Toda-Yamamoto (TY) causality test is a modified Wald procedure for testing Granger causality in vector autoregressions (VARs) estimated in levels, even when variables are nonstationary or cointegrated. By intentionally over-fitting the VAR with extra lags equal to the maximum integration order, it restores the standard chi-squared asymptotic distribution of the Wald statistic without requiring prior unit-root or cointegration pretesting.