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Efficient Gibbs Sampling for Markov Switching GARCH Models

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  • Monica Billio

    ()
    (Department of Economics, University Of Venice Cà Foscari)

  • Roberto Casarin

    ()
    (Department of Economics, University Of Venice Cà Foscari)

  • Anthony Osuntuyi

    ()
    (Department of Economics, University Of Venice Cà Foscari)

Abstract

We develop efficient simulation techniques for Bayesian inference on switching GARCH models. Our contribution to existing literature is manifold. First, we discuss different multi-move sampling techniques for Markov Switching (MS) state space models with particular attention to MS-GARCH models. Our multi-move sampling strategy is based on the Forward Filtering Backward Sampling (FFBS) applied to an approximation of MS-GARCH. Another important contribution is the use of multi-point samplers, such as the Multiple-Try Metropolis (MTM) and the Multiple trial Metropolize Independent Sampler, in combination with FFBS for the MS-GARCH process. In this sense we ex- tend to the MS state space models the work of So [2006] on efficient MTM sampler for continuous state space models. Finally, we suggest to further improve the sampler efficiency by introducing the antithetic sampling of Craiu and Meng [2005] and Craiu and Lemieux [2007] within the FFBS. Our simulation experiments on MS-GARCH model show that our multi-point and multi-move strategies allow the sampler to gain efficiency when compared with single-move Gibbs sampling.

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Bibliographic Info

Paper provided by Department of Economics, University of Venice "Ca' Foscari" in its series Working Papers with number 2012:35.

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Length: 40
Date of creation: 2012
Date of revision:
Handle: RePEc:ven:wpaper:2012:35

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Related research

Keywords: Bayesian inference; GARCH; Markov switching; Multiple-try Metropolis;

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References

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  1. Roberto Casarin & Radu Craiu & Fabrizio Leisen, 2011. "Interacting multiple -- Try algorithms with different proposal distributions," Statistics and Econometrics Working Papers ws110402, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  3. Michael Dueker, 1995. "Markov switching in GARCH processes and mean reverting stock market volatility," Working Papers 1994-015, Federal Reserve Bank of St. Louis.
  4. BAUWENS, Luc & PREMINGER, Arie & ROMBOUTS, Jeroen V.K., 2007. "Theory and inference for a Markov switching GARCH model," CORE Discussion Papers 2007055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-34, April.
  6. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  7. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
  8. Billio, M. & Monfort, A. & Robert, C. P., 1999. "Bayesian estimation of switching ARMA models," Journal of Econometrics, Elsevier, vol. 93(2), pages 229-255, December.
  9. Marcucci Juri, 2005. "Forecasting Stock Market Volatility with Regime-Switching GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-55, December.
  10. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
  11. Robert J. Elliott & John W. Lau & Hong Miao & Tak Kuen Siu, 2012. "Viterbi-Based Estimation for Markov Switching GARCH Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(3), pages 219-231, August.
  12. Abramson, Ari & Cohen, Israel, 2007. "On The Stationarity Of Markov-Switching Garch Processes," Econometric Theory, Cambridge University Press, vol. 23(03), pages 485-500, June.
  13. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  15. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  16. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-16, July.
  17. Jan Henneke & Svetlozar Rachev & Frank Fabozzi & Metodi Nikolov, 2011. "MCMC-based estimation of Markov Switching ARMA-GARCH models," Applied Economics, Taylor & Francis Journals, vol. 43(3), pages 259-271.
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