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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. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  8. Dhiman Das, 2004. "A Bayesian algorithm for a Markov Switching GARCH model," Computing in Economics and Finance 2004 30, Society for Computational Economics.
  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. 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.
  11. 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.
  12. 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.
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Citations

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Cited by:
  1. Bohl, Martin T. & Essid, Badye & Siklos, Pierre L., 2012. "Do short selling restrictions destabilize stock markets? Lessons from Taiwan," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(2), pages 198-206.
  2. L. Bauwens & E. Otranto, 2013. "Modeling the Dependence of Conditional Correlations on Volatility," Working Paper CRENoS 201304, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  3. BAUWENS, Luc & DUFAYS, Arnaud & ROMBOUTS, Jeroen V.K., 2011. "Marginal likelihood for Markov-switching and change-point GARCH models," CORE Discussion Papers 2011013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Gilbert Colletaz & Christophe Hurlin & Christophe Pérignon, 2012. "The Risk Map: A New Tool for Validating Risk Models," Working Papers halshs-00746273, HAL.
  5. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
  6. Yin-Wong Cheung & Sang-Kuck Chung, 2011. "A Long Memory Model with Normal Mixture GARCH," Computational Economics, Society for Computational Economics, vol. 38(4), pages 517-539, November.
  7. David Ardia & Lennart F. Hoogerheide, 2010. "Efficient Bayesian Estimation and Combination of GARCH-Type Models," Tinbergen Institute Discussion Papers 10-046/4, Tinbergen Institute.
  8. Monica Billio & Roberto Casarin & Anthony Osuntuyi, 2012. "Efficient Gibbs Sampling for Markov Switching GARCH Models," Working Papers 2012:35, Department of Economics, University of Venice "Ca' Foscari".
  9. Monica Billio & Maddalena Cavicchioli, 2013. "“Markov Switching Models for Volatility: Filtering, Approximation and Duality”," Working Papers 2013:24, Department of Economics, University of Venice "Ca' Foscari".
  10. Szabolcs Blazsek & Anna Downarowicz, 2008. "Regime switching models of hedge fund returns," Faculty Working Papers 12/08, School of Economics and Business Administration, University of Navarra.
  11. Gelman, Sergey & Wilfling, Bernd, 2009. "Markov-switching in target stocks during takeover bids," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 745-758, December.
  12. Almeida, R.J. & Basturk, N. & Kaymak, U. & Costa Sousa, J.M., 2013. "Estimation of flexible fuzzy GARCH models for conditional density estimation," ERIM Report Series Research in Management ERS-2013-013-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
  13. Pierre-Julien Trombe & Pierre Pinson & Henrik Madsen, 2012. "A General Probabilistic Forecasting Framework for Offshore Wind Power Fluctuations," Energies, MDPI, Open Access Journal, vol. 5(3), pages 621-657, March.

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