Σύγκριση μεθόδων

	Έλεγχος Αιτιότητας Granger Dolado-Lütkepohl	Δοκιμή Αιτιότητας Granger	Έλεγχος Αιτιότητας κατά Granger των Toda-Yamamoto
Πεδίο	Οικονομετρία	Οικονομετρία	Οικονομετρία
Οικογένεια	Hypothesis test	Regression model	Hypothesis test
Έτος προέλευσης	1996	1969	1995
Δημιουργός	Juan Dolado & Helmut Lütkepohl	Clive W. J. Granger	Hiro Toda & Taku Yamamoto
Τύπος	Modified Wald test for Granger causality in possibly integrated or cointegrated VAR systems	Time-series predictive causality test	Modified Wald test on augmented VAR
Θεμελιώδης πηγή	Dolado, J. J., & Lütkepohl, H. (1996). Making Wald tests work for cointegrated VAR systems. Econometric Reviews, 15(4), 369–386.	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	DL Causality Test, Modified Wald Causality Test, Augmented VAR Causality Test, Dolado-Lütkepohl Testi	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	2	5	3
Σύνοψη	The Dolado-Lütkepohl (DL) test, introduced by Dolado and Lütkepohl (1996), is a modified Wald procedure for testing Granger causality in vector autoregressive (VAR) systems whose variables may be integrated or cointegrated. By fitting a VAR of slightly higher order than necessary and restricting the Wald statistic to the first p lag blocks, the test recovers the standard chi-squared limiting distribution without requiring pre-testing for cointegration or transformation to error-correction form.	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.