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Exact Maximum Likelihood and Bayesian Estimation of the Stochastic Volatility Model

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  • Motta, Anderson C. O.
  • Hotta, Luiz K.
Abstract
This paper considers the classical and Bayesian approaches to the estimation of the stochastic volatility (SV) model. The estimation procedures rely heavily on the fact that SV model can be written in the State Space Form (SSF) with non-Ga ussian disturbances. The first widely employed estimation procedure to use this model was the quasi-maximum likelihood estimator proposed by Harvey et al. The Bayesian approach was proposed by Jacquier et al.(1994). Lately, many papers have appeared in the literature dealing with non-Gaussian state space models which directly influenced the estimation of the SV model. Some of these methods proposed to estimate the SV model are compared using the Sao Paulo stock exchange index (IBOVESPA) and simulated series. The influence of outliers is also considered.

Suggested Citation

  • Motta, Anderson C. O. & Hotta, Luiz K., 2003. "Exact Maximum Likelihood and Bayesian Estimation of the Stochastic Volatility Model," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 23(2), November.
    • Handle: RePEc:sbe:breart:v:23:y:2003:i:2:a:2724
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    References listed on IDEAS

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    1. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non‐Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
    2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    3. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    4. Tanizaki, Hisashi & Mariano, Roberto S, 1994. "Prediction, Filtering and Smoothing in Non-linear and Non-normal Cases Using Monte Carlo Integration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(2), pages 163-179, April-Jun.
    5. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    6. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    7. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    8. 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.
    9. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    10. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    11. Ruiz, Esther, 1994. "Quasi-maximum likelihood estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 63(1), pages 289-306, July.
    12. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    13. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    14. 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.
    15. Tanizaki, Hisashi & Mariano, Roberto S., 1998. "Nonlinear and non-Gaussian state-space modeling with Monte Carlo simulations," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 263-290.
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