Deviance Information Criterion as a Model Comparison Criterion for Stochastic Volatility Models

Bayesian methods have proven very efficient in estimating parameters of stochastic volatility (SV) models for analysing financial time series. Recent work extends the basic stochastic volatility model to include heavy-tailed error distributions, covariates, leverage effects, and jump components. Hierarchical Bayesian methods (usually implemented via state-of-the-art Markov chain Monte Carlo methods for posterior computation) allow fitting of such complex models. However, a formal model comparison via Bayes factors is difficult because the marginalization constants are not readily available. Bayesian modelcomparison using the Schwarz criterion as a Bayes factor approximation requires the specification of the number of free parameters in the model. This number of free parameters, or degrees of freedom, is not well defined in stochastic volatility models. The main objective of this paper is to demonstrate that model selection within the class of SV models is better performed using the deviance information criterion (DIC). DIC is a recently developed information criterion designed for complex hierarchical models with possibly improper prior distributions. It combines a measure of fit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different SV models using simulated data and daily returns data on the S&P 100 index.