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Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion

Author

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

Suggested Citation

  • Joshua C.C. Chan & Angelia L. Grant, 2014. "Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion," CAMA Working Papers 2014-51, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2014-51
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    File URL: https://cama.crawford.anu.edu.au/sites/default/files/publication/cama_crawford_anu_edu_au/2014-07/51_2014_chan_grant.pdf
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Modeling energy price dynamics: GARCH versus stochastic volatility," Energy Economics, Elsevier, vol. 54(C), pages 182-189.
    2. Tao Zeng & Yong Li & Jun Yu, 2014. "Deviance Information Criterion for Comparing VAR Models," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 615-637, Emerald Group Publishing Limited.
    3. Joshua C. C. Chan, 2020. "Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(1), pages 68-79, January.
    4. Chan, Joshua C.C. & Grant, Angelia L., 2015. "Pitfalls of estimating the marginal likelihood using the modified harmonic mean," Economics Letters, Elsevier, vol. 131(C), pages 29-33.
    5. Lu Yang & Shigeyuki Hamori, 2018. "Modeling The Dynamics Of International Agricultural Commodity Prices: A Comparison Of Garch And Stochastic Volatility Models," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 1-20, September.
    6. Nonejad Nima, 2015. "Particle Gibbs with ancestor sampling for stochastic volatility models with: heavy tails, in mean effects, leverage, serial dependence and structural breaks," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 561-584, December.
    7. Abdelhakim Aknouche, 2017. "Periodic autoregressive stochastic volatility," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 139-177, July.
    8. Joshua C. C. Chan, 2018. "Specification tests for time-varying parameter models with stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 807-823, September.
    9. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    10. Aknouche, Abdelhakim, 2013. "Periodic autoregressive stochastic volatility," MPRA Paper 69571, University Library of Munich, Germany, revised 2015.

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    More about this item

    Keywords

    Bayesian model comparison; nonlinear state space; DIC; jumps; moving average; S&P 500;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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