Bayesian semiparametric stochastic volatility modeling

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 innovations, nonparametric Bayesian methods are used to flexibly model the distribution’s skewness and kurtosis while volatility dynamics follow a parametric structure. Our Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented 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. ∗We thank the seminar participants at the 24th Canadian Econometric Study Group Conference held in Montreal, the 7th All-Georgia Conference held at the Federal Reserve Bank of Atlanta, the RCEA conference on Econometrics 2007, Rimini, Italy, and Oregon State University. In addition, we express appreciation for the comments and suggestions of Thanasis Stengos and George Tauchen. Maheu is grateful to the SSHRC for financial support. The views expressed here are ours and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.