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Theory and inference for a Markov switching GARCH model

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Author Info

  • BAUWENS, Luc

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • PREMINGER, Arie
  • ROMBOUTS, Jeroen V.K.

Abstract

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We illustrate the model on SP500 daily returns.

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File URL: http://www.uclouvain.be/cps/ucl/doc/core/documents/coredp2007_55.pdf
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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2007055.

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Date of creation: 01 Aug 2007
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Handle: RePEc:cor:louvco:2007055

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Keywords: GARCH; Markov-switching; Bayesian inference;

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References

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  1. 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.
  2. Yang, Minxian, 2000. "Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients," Econometric Theory, Cambridge University Press, vol. 16(01), pages 23-43, February.
  3. 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.
  4. Michael Dueker, 1995. "Markov switching in GARCH processes and mean reverting stock market volatility," Working Papers 1994-015, Federal Reserve Bank of St. Louis.
  5. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
  6. 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.
  7. Dhiman Das, 2004. "A Bayesian algorithm for a Markov Switching GARCH model," Computing in Economics and Finance 2004 30, Society for Computational Economics.
  8. Christian Francq & Michel Roussignol & Jean-Michel Zakoian, 1998. "Conditional heteroskedasticity driven by hidden Markov chains," SFB 373 Discussion Papers 1998,86, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  9. Dhiman Das & B.Hark Yoo, 2004. "A Bayesian MCMC Algorithm for Markov Switching GARCH models," Econometric Society 2004 Far Eastern Meetings 451, Econometric Society.
  10. Bollen, Nicolas P. B. & Gray, Stephen F. & Whaley, Robert E., 2000. "Regime switching in foreign exchange rates: Evidence from currency option prices," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 239-276.
  11. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  12. Francq, Christian & Zako an, Jean-Michel, 2002. "Comments On The Paper By Minxian Yang:," Econometric Theory, Cambridge University Press, vol. 18(03), pages 815-818, June.
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