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

Author Info

  • 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.

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File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/231.pdf
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Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-221.

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Length: 31 pages
Date of creation: May 2010
Date of revision:
Handle: RePEc:cfi:fseres:cf221
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  1. Yasuhiro Omori & Toshiaki Watanabe, 2007. "Block Sampler and Posterior Mode Estimation for Asymmetric Stochastic Volatility Models," CIRJE F-Series CIRJE-F-507, CIRJE, Faculty of Economics, University of Tokyo.
  2. Manabu Asai & Massimiliano Caporin & Michael McAleer, 2010. "Block Structure Multivariate Stochastic Volatility Models," Working Papers in Economics 10/24, University of Canterbury, Department of Economics and Finance.
  3. Tsunehiro Ishihara & Yasuhiro Omori, 2009. "Multivariate Stochastic Volatility with Cross Leverage," CARF F-Series CARF-F-191, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  4. Carmen Broto & Esther Ruiz, 2002. "Estimation Methods For Stochastic Volatility Models: A Survey," Statistics and Econometrics Working Papers ws025414, Universidad Carlos III, Departamento de Estadística y Econometría.
  5. 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.
  6. Takahashi, Makoto & Omori, Yasuhiro & Watanabe, Toshiaki, 2009. "Estimating stochastic volatility models using daily returns and realized volatility simultaneously," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2404-2426, April.
  7. Toshiaki Watanabe, 2004. "A multi-move sampler for estimating non-Gaussian time series models: Comments on Shephard & Pitt (1997)," Biometrika, Biometrika Trust, vol. 91(1), pages 246-248, March.
  8. 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.
  9. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
  10. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
  11. Nakajima, Jouchi & Omori, Yasuhiro, 2009. "Leverage, heavy-tails and correlated jumps in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2335-2353, April.
  12. Manabu Asai & Michael McAleer, 2006. "Asymmetric Multivariate Stochastic Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 453-473.
  13. Eric Jacquier & Nicholas G. Polson & Peter Rossi, . "Stochastic Volatility: Univariate and Multivariate Extensions," Rodney L. White Center for Financial Research Working Papers 19-95, Wharton School Rodney L. White Center for Financial Research.
  14. David Chan & Robert Kohn & Chris Kirby, 2006. "Multivariate Stochastic Volatility Models with Correlated Errors," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 245-274.
  15. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
  16. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
  17. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
  18. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  19. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
  20. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
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Cited by:

  1. António Alberto Santos & João Andrade, 2014. "Stochastic Volatility Estimation with GPU Computing," GEMF Working Papers 2014-10, GEMF - Faculdade de Economia, Universidade de Coimbra.
  2. Jouchi Nakajima & Yasuhiro Omori, 2010. "Stochastic Volatility Model with Leverage and Asymmetrically Heavy-tailed Error Using GH Skew Student's t-distribution," Global COE Hi-Stat Discussion Paper Series gd09-124, Institute of Economic Research, Hitotsubashi University.
  3. Yuta Kurose & Yasuhiro Omori, 2014. "Dynamic Equicorrelation Stochastic Volatility," CIRJE F-Series CIRJE-F-941, CIRJE, Faculty of Economics, University of Tokyo.
  4. 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.
  5. 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.
  6. Yuta Kurose & Yasuhiro Omori, 2013. "Dynamic Equicorrelation Stochastic Volatility," CIRJE F-Series CIRJE-F-907, CIRJE, Faculty of Economics, University of Tokyo.

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