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Leverage, heavy-tails and correlated jumps in stochastic volatility models

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  • Nakajima, Jouchi
  • Omori, Yasuhiro

Abstract

Efficient and fast Markov chain Monte Carlo estimation methods for the stochastic volatility model with leverage effects, heavy-tailed errors and jump components, and for the stochastic volatility model with correlated jumps are proposed. The methods are illustrated using simulated data and are applied to analyze daily stock returns data on S&P500 index and TOPIX. Model comparisons are conducted based on the marginal likelihood for various SV models including the superposition model.

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File URL: http://www.sciencedirect.com/science/article/B6V8V-4S2F5GD-2/2/bbabb9344a77b3a9dc6ec044dc8d3fc3
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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 53 (2009)
Issue (Month): 6 (April)
Pages: 2335-2353

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Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2335-2353

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Web page: http://www.elsevier.com/locate/csda

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  1. Chan, Wing H & Maheu, John M, 2002. "Conditional Jump Dynamics in Stock Market Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 377-89, July.
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  3. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
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  7. 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.
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  9. Raggi, Davide & Bordignon, Silvano, 2006. "Comparing stochastic volatility models through Monte Carlo simulations," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1678-1699, April.
  10. 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.
  11. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
  12. Bartolucci, F. & De Luca, G., 2003. "Likelihood-based inference for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 445-449, March.
  13. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
  14. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  15. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
  16. Masahito Kobayashi, 2005. "Testing for Volatility Jumps in the Stochastic Volatility Process," Asia-Pacific Financial Markets, Springer, vol. 12(2), pages 143-157, June.
  17. Siddhartha Chib & Ivan Jeliazkov, 2005. "Accept-reject Metropolis-Hastings sampling and marginal likelihood estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 30-44.
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Citations

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Cited by:
  1. BAUWENS, Luc & ROMBOUTS, Jeroen, 2009. "On marginal likelihood computation in change-point models," CORE Discussion Papers 2009061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Shinichiro Shirota & Takayuki Hizu & Yasuhiro Omori, 2012. "Realized stochastic volatility with leverage and long memory," CIRJE F-Series CIRJE-F-869, CIRJE, Faculty of Economics, University of Tokyo.
  3. Tsunehiro Ishihara & Yasuhiro Omori, 2010. "Efficient Bayesian Estimation of a Multivariate Stochastic Volatility Model with Cross Leverage and Heavy-Tailed Errors," CARF F-Series CARF-F-221, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  4. 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.
  5. António Alberto Santos & João Andrade, 2014. "Stochastic Volatility Estimation with GPU Computing," GEMF Working Papers 2014-10, GEMF - Faculdade de Economia, Universidade de Coimbra.
  6. Xiuping Mao & Esther Ruiz & Helena Veiga, 2013. "One for all : nesting asymmetric stochastic volatility models," Statistics and Econometrics Working Papers ws131110, Universidad Carlos III, Departamento de Estadística y Econometría.
  7. Trojan, Sebastian, 2013. "Regime Switching Stochastic Volatility with Skew, Fat Tails and Leverage using Returns and Realized Volatility Contemporaneously," Economics Working Paper Series 1341, University of St. Gallen, School of Economics and Political Science.
  8. Shirota, Shinichiro & Hizu, Takayuki & Omori, Yasuhiro, 2014. "Realized stochastic volatility with leverage and long memory," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 618-641.
  9. Jouchi Nakajima & Yasuhiro Omori, 2010. "Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution Models," CIRJE F-Series CIRJE-F-738, CIRJE, Faculty of Economics, University of Tokyo.

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