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Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student?s t-Distribution

Author

Listed:
  • Jouchi Nakajima

    (Department of Statistical Science, Duke University)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

Abstract

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student?s t-error distribution is described where we first consider an asymmetric heavy-tailed error and leverage effects. An efficient Markov chain Monte Carlo estimation method is described that exploits a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as the mixing distribution. The proposed method is illustrated using simulated data, daily S&P500 and TOPIX stock returns. The models for stock returns are compared based on the marginal likelihood in the empirical study. There is strong evidence in the stock returns high leverage and an asymmetric heavy-tailed distribution. Furthermore, a prior sensitivity analysis is conducted whether the results obtained are robust with respect to the choice of the priors.

Suggested Citation

  • Jouchi Nakajima & Yasuhiro Omori, 2010. "Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student?s t-Distribution," CARF F-Series CARF-F-215, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  • Handle: RePEc:cfi:fseres:cf215
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    References listed on IDEAS

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    Cited by:

    1. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    2. Lopes Moreira Da Veiga, María Helena & Ruiz Ortega, Esther & Mao, Xiuping, 2013. "One for all : nesting asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws131110, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2016. "Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution," International Journal of Forecasting, Elsevier, vol. 32(2), pages 437-457.
    4. Cabral, Celso Rômulo Barbosa & da-Silva, Cibele Queiroz & Migon, Helio S., 2014. "A dynamic linear model with extended skew-normal for the initial distribution of the state parameter," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 64-80.
    5. Deschamps, P., 2015. "Alternative Formulation of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy-Tailed Errors," CORE Discussion Papers 2015020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3674-3689.
    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. Takahashi, Makoto & Omori, Yasuhiro & Watanabe, Toshiaki, 2013. "News impact curve for stochastic volatility models," Economics Letters, Elsevier, vol. 120(1), pages 130-134.
    9. Lopes Moreira Da Veiga, María Helena & Ruiz Ortega, Esther & Mao, Xiuping, 2014. "Score driven asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws142618, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Roland Langrock & Théo Michelot & Alexander Sohn & Thomas Kneib, 2015. "Semiparametric stochastic volatility modelling using penalized splines," Computational Statistics, Springer, vol. 30(2), pages 517-537, June.
    11. Felicia Ramona Birău, 2012. "Stochastic Volatility Models For Financial Time Series Analysis," Anale. Seria Stiinte Economice. Timisoara, Faculty of Economics, Tibiscus University in Timisoara, vol. 0, pages 472-475, November.
    12. Patricia Lengua & Cristian Bayes & Gabriel Rodríguez, 2015. " A Stochastic Volatility Model with GH Skew Student’s t-Distribution: Application to Latin-American Stock Returns," Documentos de Trabajo / Working Papers 2015-405, Departamento de Economía - Pontificia Universidad Católica del Perú.
    13. 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.
    14. Genya Kobayashi, 2016. "Skew exponential power stochastic volatility model for analysis of skewness, non-normal tails, quantiles and expectiles," Computational Statistics, Springer, vol. 31(1), pages 49-88, March.
    15. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2017. "Creating Investment Scheme with State Space Modeling," CIRJE F-Series CIRJE-F-1038, CIRJE, Faculty of Economics, University of Tokyo.
    16. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2017. "Creating Investment Scheme with State Space Modeling," CARF F-Series cf406, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    17. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.

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