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Theory and inference for a Markov switching Garch model

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  • Luc Bauwens
  • Arie Preminger
  • Jeroen V.K. Rombouts

    ()
    (IEA, HEC Montréal)

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.hec.ca/iea/cahiers/2007/iea0709_jrombouts.pdf
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Bibliographic Info

Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number 07-09.

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Length: 30 pages
Date of creation: Aug 2007
Date of revision:
Handle: RePEc:iea:carech:0709

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Postal: Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7
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Keywords: GARCH; Markov-switching; Bayesian inference.;

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References

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  1. Dhiman Das & B.Hark Yoo, 2004. "A Bayesian MCMC Algorithm for Markov Switching GARCH models," Econometric Society 2004 Far Eastern Meetings 451, Econometric Society.
  2. 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.
  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. Dhiman Das, 2004. "A Bayesian algorithm for a Markov Switching GARCH model," Computing in Economics and Finance 2004 30, Society for Computational Economics.
  5. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  6. 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.
  7. Dueker, Michael J, 1997. "Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 26-34, January.
  8. 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.
  9. 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.
  10. Christian Francq & Michel Roussignol & Jean-Michel Zakoïan, 1998. "Conditional Heteroskedasticity Driven by Hidden Markov Chains," Working Papers 98-45, Centre de Recherche en Economie et Statistique.
  11. 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.
  12. 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.
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