Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion
25 Pages Posted: 12 Jul 2014 Last revised: 21 Jul 2014
Date Written: July 1, 2014
Abstract
The deviance information criterion (DIC) has been widely used for Bayesian model comparison. In particular, a popular metric for comparing stochastic volatility models is the DIC based on the conditional likelihood — obtained by conditioning on the latent variables. However, some recent studies have argued against the use of the conditional DIC on both theoretical and practical grounds. We show via a Monte Carlo study that the conditional DIC tends to favor overfitted models, whereas the DIC calculated using the observed-data likelihood — obtained by integrating out the latent variables — seems to perform well. The main challenge for obtaining the latter DIC for stochastic volatility models is that the observed-data likelihoods are not available in closed-form. To overcome this difficulty, we propose fast algorithms for estimating the observed-data likelihoods for a variety of stochastic volatility models using importance sampling. We demonstrate the methodology with an application involving daily returns on the Standard & Poors (S&P) 500 index.
Keywords: Bayesian model comparison, nonlinear state space, DIC, jumps, moving average, S&P 500
JEL Classification: C11, C15, C52, C58
Suggested Citation: Suggested Citation