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Efficient Bayesian Estimation of a Multivariate Stochastic Volatility Model with Cross Leverage and Heavy-Tailed Errors

Author

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  • Tsunehiro Ishihara

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

Abstract
An efficient Bayesian estimation using a Markov chain Monte Carlo method is proposed in the case of a multivariate stochastic volatility model as a natural extension of the univariate stochastic volatility model with leverage and heavy-tailed errors. Note that we further incorporate cross-leverage effects among stock returns. Our method is based on a multi-move sampler that samples a block of latent volatility vectors. The method is presented as a multivariate stochastic volatility model with cross leverage and heavytailed errors. Its high sampling efficiency is shown using numerical examples in comparison with a single-move sampler that samples one latent volatility vector at a time, given other latent vectors and parameters. To illustrate the method, empirical analyses are provided based on five-dimensional S&P500 sector indices returns.

Suggested Citation

  • Tsunehiro Ishihara & Yasuhiro Omori, 2010. "Efficient Bayesian Estimation of a Multivariate Stochastic Volatility Model with Cross Leverage and Heavy-Tailed Errors," CIRJE F-Series CIRJE-F-746, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2010cf746
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    Cited by:

    1. Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori, 2017. "Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1248-1268, May.
    2. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    3. Kurose, Yuta & Omori, Yasuhiro, 2020. "Multiple-block dynamic equicorrelations with realized measures, leverage and endogeneity," Econometrics and Statistics, Elsevier, vol. 13(C), pages 46-68.
    4. Yuta Kurose & Yasuhiro Omori, "undated". "Multiple-lock Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1075, CIRJE, Faculty of Economics, University of Tokyo.
    5. Tsunehiro Ishihara & Yasuhiro Omori, 2017. "Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat-tailed errors and leverage," The Japanese Economic Review, Japanese Economic Association, vol. 68(1), pages 63-94, March.
    6. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
    7. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
    8. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.
    9. Yuta Kurose & Yasuhiro Omori, 2016. "Multiple-block Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1024, CIRJE, Faculty of Economics, University of Tokyo.
    10. Kurose, Yuta & Omori, Yasuhiro, 2016. "Dynamic equicorrelation stochastic volatility," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 795-813.
    11. Florian Huber & Gary Koop & Massimiliano Marcellino & Tobias Scheckel, 2024. "Bayesian modelling of VAR precision matrices using stochastic block networks," Papers 2407.16349, arXiv.org.
    12. António Alberto Santos & João Andrade, 2014. "Stochastic Volatility Estimation with GPU Computing," GEMF Working Papers 2014-10, GEMF, Faculty of Economics, University of Coimbra.
    13. Shirota, Shinichiro & Omori, Yasuhiro & F. Lopes, Hedibert. & Piao, Haixiang, 2017. "Cholesky realized stochastic volatility model," Econometrics and Statistics, Elsevier, vol. 3(C), pages 34-59.
    14. Elchin Suleymanov & Magsud Gubadli & Ulvi Yagubov, 2024. "Test of Volatile Behaviors with the Asymmetric Stochastic Volatility Model: An Implementation on Nasdaq-100," Risks, MDPI, vol. 12(5), pages 1-20, May.
    15. Tsunehiro Ishihara & Yasuhiro Omori, 2017. "Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat-tailed errors and leverage," The Japanese Economic Review, Springer, vol. 68(1), pages 63-94, March.
    16. Trojan, Sebastian, 2014. "Multivariate Stochastic Volatility with Dynamic Cross Leverage," Economics Working Paper Series 1424, University of St. Gallen, School of Economics and Political Science.

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