Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean

Valentin Patilea

Code and Data Abstract

The code provides Wald tests results for testing linear Granger causality in mean in the framework of VAR models with non constant variance. A summary on bandwidth selection and the minimum eigenvalues of the estimated volatilities is displayed. The series have to be centered before proceeding to the tests. Note that the adequacy of the VAR model has to be tested before using the modified portmanteau tests available on this companion website.

Paper Abstract

Linear Vector AutoRegressive (VAR) models where the innovations could be unconditionally heteroscedastic and serially dependent are considered. The volatility structure is deterministic and quite general, including breaks or trending variances as special cases. In this framework we propose Ordinary Least Squares (OLS), Generalized Least Squares (GLS) and Adaptive Least Squares (ALS) procedures. The GLS estimator requires the knowledge of the time-varying variance structure while in the ALS approach the unknown variance is estimated by kernel smoothing with the outer product of the OLS residuals vectors. Different bandwidths for the different cells of the time-varying variance matrix are also allowed. We derive the asymptotic distribution of the proposed estimators for the VAR model coefficients and compare their properties. In particular we show that the ALS estimator is asymptotically equivalent to the infeasible GLS estimator. This asymptotic equivalence is obtained uniformly with respect to the bandwidth(s) in a given range and hence justifies data-driven bandwidth rules. Using these results we build Wald tests for the linear Granger causality in mean which are adapted to VAR processes driven by errors with a non stationary volatility. It is also shown that the commonly used standard Wald test for the linear Granger causality in mean is potentially unreliable in our framework (incorrect level and lower asymptotic power). Monte Carlo and real-data experiments illustrate the use of the different estimation approaches for the analysis of VAR models with time-varying variance innovations.

Valentin Patilea. "Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean." IRMAR-INSA and CREST ENSAI (2010).     Retrieved 07/30/2021 from

Page Owner

created 11/12/2013

modified 01/16/2014

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