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Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion

  • Joshua C.C. Chan
  • Angelia L. Grant

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.

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Paper provided by Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University in its series CAMA Working Papers with number 2014-51.

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Length: 25 pages
Date of creation: Jul 2014
Date of revision:
Handle: RePEc:een:camaaa:2014-51
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  1. Jouchi Nakajima & Yasuhiro Omori, 2009. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student's t-distribution," CARF F-Series CARF-F-199, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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  3. Joshua C.C. Chan, 2013. "Moving Average Stochastic Volatility Models with Application to Inflation Forecast," CAMA Working Papers 2013-31, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  4. Joshua C.C. Chan & Angelia L. Grant, 2014. "Fast Computation of the Deviance Information Criterion for Latent Variable Models," CAMA Working Papers 2014-09, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
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  14. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
  15. Jun Yu & Renate Meyer, 2004. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Working Papers 23-2004, Singapore Management University, School of Economics.
  16. Tsiotas, Georgios, 2012. "On generalised asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 151-172, January.
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