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Theory and inference for a Markov switching GARCH model

Author

Listed:
  • Luc, BAUWENS

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Department of Economics)

  • Arie, PREMINGER

    (University of Haifa, Israel, Department of Economics)

  • Jeroen, ROMBOUTS

    (Institute of Applied Economics at HEC Montreal, CIRPEE, CREF, CORE (Université catholique de Louvain), CREF)

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 existene 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, ROMBOUTS, 2007. "Theory and inference for a Markov switching GARCH model," Discussion Papers (ECON - Département des Sciences Economiques) 2007033, Université catholique de Louvain, Département des Sciences Economiques.
  • Handle: RePEc:ctl:louvec:2007033
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    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.
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    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.
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    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

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