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Atlanta Fed Working Papers

Bayesian Semiparametric Stochastic Volatility Modeling

Mark J. Jensen and John M. Maheu
Working Paper 2008-15
June 2008

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This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, we use nonparametric Bayesian methods to flexibly model the skewness and kurtosis of the distribution while continuing to model the dynamics of volatility with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. We present a Markov chain Monte Carlo sampling approach to estimation with theoretical and computational issues for simulation from the posterior predictive distributions. The new model is assessed based on simulation evidence, an empirical example, and comparison to parametric models.

JEL classification: C11, C14, C53

Key words: Bayesian nonparametrics, Dirichlet process mixture prior, Markov chain Monte Carlo, mixture models, stochastic volatility


The authors thank the seminar participants at the Canadian Econometric Study Group conference held in Montreal; the All-Georgia Conference held at the Federal Reserve Bank of Atlanta; the Rimini Center for Economic Analysis's 2007 Conference on Econometrics, held in Rimini, Italy; the annual symposium of the Society for Nonlinear Dynamics and Econometrics held at the Federal Reserve Bank of San Francisco; and the Department of Economics at Oregon State University. They also appreciate the comments and suggestions of Thanasis Stengos and George Tauchen. 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, Associate Professor, Department of Economics, University of Toronto, 150 St. George Street, Toronto, Canada, M5S 3G7, 416-978-1495, jmaheu@chass.utoronto.ca.

For further information, contact the Public Affairs Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, Georgia 30309-4470, 404-498-8020.