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	Test di causalità di Granger di Dolado-Lütkepohl	Modello di Autoregressione Vettoriale (VAR)
Campo	Econometria	Econometria
Famiglia	Hypothesis test	Regression model
Anno di origine	1996	2005
Ideatore	Juan Dolado & Helmut Lütkepohl	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Tipo	Modified Wald test for Granger causality in possibly integrated or cointegrated VAR systems	Multivariate time-series model
Fonte seminale	Dolado, J. J., & Lütkepohl, H. (1996). Making Wald tests work for cointegrated VAR systems. Econometric Reviews, 15(4), 369–386.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
Alias	DL Causality Test, Modified Wald Causality Test, Augmented VAR Causality Test, Dolado-Lütkepohl Testi	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Correlati	2	4
Sintesi	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.	Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005).