Abstract:
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.
