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Atlanta Fed Working Papers


Bayesian Semiparametric Multivariate GARCH Modeling

Mark J. Jensen and John M. Maheu
Working Paper 2012-9
July 2012

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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.

JEL classification: C11, C14, C53, C58

Key words: Bayesian nonparametrics, cumulative Bayes factor, Dirichlet process mixture, forecasting, infinite mixture model, MCMC, slice sampler


The authors thank Anatoliy Belaygorod, Sid Chib, James MacKinnon, Bill McCausland, and Benoit Perron for helpful comments and suggestions, and they are grateful 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. Maheu is grateful to the Social Sciences and Humanities Research Council for financial support. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Mark J. Jensen, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8019, mark.jensen@atl.frb.org, or John M. Maheu, Department of Economics, University of Toronto, Canada, and RCEA, Italy, 416-978-1495, jmaheu@chass.utoronto.ca.

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