IDEAS home Printed from https://ideas.repec.org/p/lvl/lacicr/0733.html
   My bibliography  Save this paper

Theory and Inference for a Markov-Switching GARCH Model

Author

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

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.

Suggested Citation

  • Luc Bauwens & Arie Preminger & Jeroen V.K. Rombouts, 2007. "Theory and Inference for a Markov-Switching GARCH Model," Cahiers de recherche 0733, CIRPEE.
    • Handle: RePEc:lvl:lacicr:0733
    as

    Download full text from publisher

    File URL: http://www.cirpee.org/fileadmin/documents/Cahiers_2007/CIRPEE07-33.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Christian Francq & Michel Roussignol & Jean‐Michel Zakoian, 2001. "Conditional Heteroskedasticity Driven by Hidden Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 197-220, March.
    2. Francq, Christian & Zakoïan, Jean-Michel, 2002. "Comments On The Paper By Minxian Yang: “Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients”," Econometric Theory, Cambridge University Press, vol. 18(3), pages 815-818, June.
    3. 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.
    4. Dhiman Das & B.Hark Yoo, 2004. "A Bayesian MCMC Algorithm for Markov Switching GARCH models," Econometric Society 2004 North American Summer Meetings 179, Econometric Society.
    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. 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.
    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. Abramson, Ari & Cohen, Israel, 2007. "On The Stationarity Of Markov-Switching Garch Processes," Econometric Theory, Cambridge University Press, vol. 23(3), pages 485-500, June.
    9. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    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. Yang, Minxian, 2000. "Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients," Econometric Theory, Cambridge University Press, vol. 16(1), pages 23-43, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Heidari , Hassan & Refah-Kahriz, Arash & Hashemi Berenjabadi, Nayyer, 2018. "Dynamic Relationship between Macroeconomic Variables and Stock Return Volatility in Tehran Stock Exchange: Multivariate MS ARMA GARCH Approach," Quarterly Journal of Applied Theories of Economics, Faculty of Economics, Management and Business, University of Tabriz, vol. 5(2), pages 223-250, August.
    3. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    4. Szabolcs Blazsek & Anna Downarowicz, 2013. "Forecasting hedge fund volatility: a Markov regime-switching approach," The European Journal of Finance, Taylor & Francis Journals, vol. 19(4), pages 243-275, April.
    5. Luc, BAUWENS & Arie, PREMINGER & Jeroen, ROMBOUTS, 2006. "Regime switching GARCH models," Discussion Papers (ECON - Département des Sciences Economiques) 2006006, Université catholique de Louvain, Département des Sciences Economiques.
    6. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    7. Kuang-Liang Chang, 2011. "The optimal value-at-risk hedging strategy under bivariate regime switching ARCH framework," Applied Economics, Taylor & Francis Journals, vol. 43(21), pages 2627-2640.
    8. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    9. 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.
    10. 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.
    11. Ataurima Arellano, Miguel & Rodríguez, Gabriel, 2020. "Empirical modeling of high-income and emerging stock and Forex market return volatility using Markov-switching GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    12. repec:bgu:wpaper:0605 is not listed on IDEAS
    13. Kramer, Walter & Azamo, Baudouin Tameze, 2007. "Structural change and estimated persistence in the GARCH(1,1)-model," Economics Letters, Elsevier, vol. 97(1), pages 17-23, October.
    14. 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".
    15. King, Daniel & Botha, Ferdi, 2015. "Modelling stock return volatility dynamics in selected African markets," Economic Modelling, Elsevier, vol. 45(C), pages 50-73.
    16. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
    17. Azamo, Baudouin Tameze & Krämer, Walter, 2006. "Structural Change and long memory in the GARCH(1,1)-model," Technical Reports 2006,33, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    18. 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.
    19. Levy, Moshe & Kaplanski, Guy, 2015. "Portfolio selection in a two-regime world," European Journal of Operational Research, Elsevier, vol. 242(2), pages 514-524.
    20. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    21. David Ardia, 2009. "Bayesian estimation of a Markov-switching threshold asymmetric GARCH model with Student-t innovations," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 105-126, March.

    More about this item

    Keywords

    GARCH; Markov-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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:lvl:lacicr:0733. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Manuel Paradis (email available below). General contact details of provider: https://edirc.repec.org/data/cirpeca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.