Bayesian Semiparametric Multivariate GARCH Modeling

This paper proposes a Bayesian nonparametric modeling approach for the return distribution in multivariate GARCH models. In contrast to the parametric literature the return distribution can display general forms of asymmetry and thick tails. An infinite mixture of multivariate normals is given a flexible Dirichlet process prior. The GARCH functional form enters into each of the components of this mixture. We discuss conjugate methods that allow for scale mixtures and nonconjugate methods which provide mixing over both the location and scale of the normal components. MCMC methods are introduced for posterior simulation and computation of the predictive density. Bayes factors and density forecasts with comparisons to GARCH models with Student-t innovations demonstrate the gains from our flexible modeling approach. ∗We are grateful to Anatoliy Belaygorod, Sid Chib, James MacKinnon, Bill McCausland, and Benoit Perron for helpful comments and suggestions, and for comments from both the conference participants of the European Seminar on Bayesian Econometrics 2011, CFE’11, the Seminar on Bayesian Inference in Econometrics and Statistics 2012 and the Symposium on Nonlinear Dynamics and Econometrics 2011 and the seminar participants at the University of Montreal and Queen’s University. The views expressed here are ours and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Maheu is grateful to the SSHRC for financial support. †Federal Reserve Bank of Atlanta, [email protected] ‡Department of Economics, University of Toronto, Canada and RCEA, Italy, [email protected].