Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion

25 Pages Posted: 12 Jul 2014 Last revised: 21 Jul 2014

See all articles by Joshua C. C. Chan

Joshua C. C. Chan

University of Technology Sydney (UTS) - UTS Business School; Purdue University

Angelia Grant

Australian National University (ANU) - Centre for Applied Macroeconomic Analysis (CAMA)

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

Chan, Joshua C. C. and Chan, Joshua C. C. and Grant, Angelia, Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion (July 1, 2014). CAMA Working Paper No. 51/2014, Available at SSRN: https://ssrn.com/abstract=2464850 or http://dx.doi.org/10.2139/ssrn.2464850

Joshua C. C. Chan (Contact Author)

University of Technology Sydney (UTS) - UTS Business School ( email )

Sydney
Australia

Purdue University

West Lafayette, IN 47907-1310
United States

Angelia Grant

Australian National University (ANU) - Centre for Applied Macroeconomic Analysis (CAMA) ( email )

ANU College of Business and Economics
Canberra, Australian Capital Territory 0200
Australia

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