Σύγκριση μεθόδων

	Αιτιότητα κατά Granger με δομικά κατάγματα	Δοκιμή Αιτιότητας Granger	Έλεγχος Αιτιότητας κατά Granger των Toda-Yamamoto
Πεδίο	Οικονομετρία	Οικονομετρία	Οικονομετρία
Οικογένεια	Regression model	Regression model	Hypothesis test
Έτος προέλευσης	1995-2010	1969	1995
Δημιουργός	Granger (1969) causality framework extended by Toda & Yamamoto (1995) and Balcilar et al. (2010)	Clive W. J. Granger	Hiro Toda & Taku Yamamoto
Τύπος	Hypothesis test / time-series model	Time-series predictive causality test	Modified Wald test on augmented VAR
Θεμελιώδης πηγή	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.
Εναλλακτικές ονομασίες	break-robust Granger causality, Granger causality under regime change, time-varying Granger causality, structural change Granger test	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
Συναφείς	3	5	3
Σύνοψη	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 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.