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Regime switching GARCH models

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Abstract
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.

Suggested Citation

  • Luc Bauwens & Arie Preminger & Jeroen V.K. Rombouts, 2006. "Regime switching GARCH models," Cahiers de recherche 06-08, HEC Montréal, Institut d'économie appliquée.
    • Handle: RePEc:iea:carech:0608
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    Cited by:

    1. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    2. Yuan, Chunming, 2011. "The exchange rate and macroeconomic determinants: Time-varying transitional dynamics," The North American Journal of Economics and Finance, Elsevier, vol. 22(2), pages 197-220, August.
    3. Lanne, Markku & Luoto, Jani, 2008. "Robustness of the risk-return relationship in the U.S. stock market," Finance Research Letters, Elsevier, vol. 5(2), pages 118-127, June.
    4. 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.
    5. Bauwens Luc & Storti Giuseppe, 2009. "A Component GARCH Model with Time Varying Weights," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-33, May.
    6. Bauwens, L. & Hafner, C.M. & Rombouts, J.V.K., 2007. "Multivariate mixed normal conditional heteroskedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3551-3566, April.
    7. Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Time-varying mixture GARCH models and asymmetric volatility," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 602-623.
    8. Nagaraj Naik & Biju R. Mohan, 2021. "Stock Price Volatility Estimation Using Regime Switching Technique-Empirical Study on the Indian Stock Market," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    9. He, Zhongfang & Maheu, John M., 2010. "Real time detection of structural breaks in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2628-2640, November.
    10. Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 326-360, Summer.
    11. Vo, Minh T., 2009. "Regime-switching stochastic volatility: Evidence from the crude oil market," Energy Economics, Elsevier, vol. 31(5), pages 779-788, September.
    12. Nyberg, Henri, 2010. "QR-GARCH-M Model for Risk-Return Tradeoff in U.S. Stock Returns and Business Cycles," MPRA Paper 23724, University Library of Munich, Germany.
    13. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
    14. Philippe Charlot & Vêlayoudom Marimoutou, 2008. "Hierarchical hidden Markov structure for dynamic correlations: the hierarchical RSDC model," Working Papers halshs-00285866, HAL.
    15. Xiufeng Yan, 2021. "Autoregressive conditional duration modelling of high frequency data," Papers 2111.02300, arXiv.org.
    16. Yuan, Chunming, 2011. "Forecasting exchange rates: The multi-state Markov-switching model with smoothing," International Review of Economics & Finance, Elsevier, vol. 20(2), pages 342-362, April.
    17. Michail Karoglou, 2010. "Breaking down the non-normality of stock returns," The European Journal of Finance, Taylor & Francis Journals, vol. 16(1), pages 79-95.
    18. Michail Karoglou & Panicos Demetriades & Siong Law, 2011. "One date, one break?," Empirical Economics, Springer, vol. 41(1), pages 7-24, August.
    19. Aloui, Chaker & Jammazi, Rania, 2009. "The effects of crude oil shocks on stock market shifts behaviour: A regime switching approach," Energy Economics, Elsevier, vol. 31(5), pages 789-799, September.
    20. Xiufeng Yan, 2021. "Multiplicative Component GARCH Model of Intraday Volatility," Papers 2111.02376, arXiv.org.

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    More about this item

    Keywords

    GARCH; regime switching; Bayesian inference.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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