Adaptive Estimation of VAR models with Time-Varying Variance: Application to Testing the VAR Order

• Activity Number: 669
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Valentin Patilea*+ and Hamdi Raissi
• Companies: CREST-ENSAI and IRMAR-INSA
• Keywords: Vector Autoregressive Model ; Kernel smoothing ; Portmateau tests

Abstract

Linear Vector AutoRegressive (VAR) models where the innovations could be unconditionally heteroscedastic are considered. 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 allowed. We derive the asymptotic distribution of the proposed estimators for the VAR coefficients and compare their properties. The ALS estimator is shown to be asymptotically equivalent to the infeasible GLS estimator. This asymptotic equivalence is obtained uniformly with respect to the bandwidth(s) and hence justifies data-driven bandwidth rules. Using these results we investigate the portmanteau tests when the innovations have time-varying variance and propose new corrected versions. The theoretical results are illustrated using a U.S. macro-economic data set.