Deviance information criterion for comparing stochastic volatility models

Abstract

Bayesian methods have been ef cient in estimating parameters of stochastic volatility models for analyzing nancial time series. Recent advances made it possible to t stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components, and heavy-tailed distributions. However, a formal model comparison via Bayes factors remains dif cult. The main objective of this article is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measure of t with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated data and daily returns data on the Standard & Poors (S&P) 100 index