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Regime switching GARCH models

We develop univariate regime-switching GARCH (RS-GARCH) models wherein the conditional variance switches in time from one GARCH process to another. The switching is governed by a time-varying probability, specified as a function of past information. We provide sufficient conditions for stationarity and existence of moments. Because of path dependence, maximum likelihood estimation is infeasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We apply this model using the NASDAQ daily return series.

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File URL: http://www.hec.ca/iea/cahiers/2006/iea0608_jrombouts.pdf
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Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number 06-08.

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Length: 26 pages
Date of creation: Jun 2006
Date of revision:
Handle: RePEc:iea:carech:0608
Contact details of provider: Postal: Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7
Phone: (514) 340-6463
Fax: (514) 340-6469
Web page: http://www.hec.ca/iea/
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  1. BAUWENS, Luc & ROMBOUTS, Jeroen V.K., 2005. "Bayesian inference for the mixed conditional heteroskedasticity model," CORE Discussion Papers 2005085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  3. 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.
  4. Markku Lanne & Pentti Saikkonen, 2003. "Modeling the U.S. Short-Term Interest Rate by Mixture Autoregressive Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 96-125.
  5. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  6. Wang, Kai-Li & Fawson, Christopher B. & Barrett, Christopher B. & McDonald, James B., 1998. "A Flexible Parametric Garch Model With An Application To Exchange Rates," Economics Research Institute, ERI Study Papers 28355, Utah State University, Economics Department.
  7. Kim, C-J., 1991. "Dynamic Linear Models with Markov-Switching," Papers 91-8, York (Canada) - Department of 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. Vlaar, Peter J G & Palm, Franz C, 1993. "The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroscedasticity, and Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 351-60, July.
  10. K. Van Dijk & Luc Bauwens & Charles Bos, 2000. "Adaptive Polar Sampling With An Application To A Bayes Measure Of Value-At-Risk," Computing in Economics and Finance 2000 145, Society for Computational Economics.
  11. Lamoureux, Christopher G & Lastrapes, William D, 1990. " Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-29, March.
  12. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  13. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
  14. 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.
  15. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 399-421.
  16. 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.
  17. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 211-250.
  18. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
  19. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  20. Luc Bauwens & Charles S. Bos & Herman K. van Dijk & Rutger D. van Oest, 2002. "Adaptive Polar Sampling," Computing in Economics and Finance 2002 307, Society for Computational Economics.
  21. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
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