Bayesian Semiparametric Stochastic Volatility Modeling

Abstract: This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of spec-ifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric 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 would like to thank the seminar participants at the 24th Canadian Econometric Study Group Conference held in Montreal, the 7th All-Georgia Conference held at the Federal Reserv