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Modeling volatility using state space models with heavy tailed distributions

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  • de Pinho, Frank M.
  • Franco, Glaura C.
  • Silva, Ralph S.

Abstract

This article deals with a non-Gaussian state space model (NGSSM) which is attractive because the likelihood can be analytically computed. The paper focuses on stochastic volatility models in the NGSSM, where the observation equation is modeled with heavy tailed distributions such as Log-gamma, Log-normal and Weibull. Parameter point estimation can be accomplished either using Bayesian or classical procedures and a simulation study shows that both methods lead to satisfactory results. In a real data application, the proposed stochastic volatility models in the NGSSM are compared with the traditional autoregressive conditionally heteroscedastic, its exponential version, and stochastic volatility models using South and North American stock price indexes.

Suggested Citation

  • de Pinho, Frank M. & Franco, Glaura C. & Silva, Ralph S., 2016. "Modeling volatility using state space models with heavy tailed distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 108-127.
    • Handle: RePEc:eee:matcom:v:119:y:2016:i:c:p:108-127
    DOI: 10.1016/j.matcom.2015.08.005
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    1. 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.
    2. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    3. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    4. Deschamps, Philippe J., 2011. "Bayesian estimation of an extended local scale stochastic volatility model," Journal of Econometrics, Elsevier, vol. 162(2), pages 369-382, June.
    5. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    6. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. 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.
    9. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
    10. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
    11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    12. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    13. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    14. 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.
    15. Deschamps, Philippe J., 2011. "Bayesian estimation of an extended local scale stochastic volatility model," Journal of Econometrics, Elsevier, vol. 162(2), pages 369-382, June.
    16. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    17. P. Vidoni, 1999. "Exponential family state space models based on a conjugate latent process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 213-221.
    18. Ferrante, Marco & Vidoni, Paolo, 1998. "Finite dimensional filters for nonlinear stochastic difference equations with multiplicative noises," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 69-81, September.
    19. 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.
    20. Dani Gamerman & Thiago Rezende Santos & Glaura C. Franco, 2013. "A Non-Gaussian Family Of State-Space Models With Exact Marginal Likelihood," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 625-645, November.
    21. 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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