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Marginal Likelihood for Markov-switching and Change-point Garch Models

Author

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  • Luc Luc

    () (Université catholique de Louvain, CORE)

  • Arnaud Dufays

    () (Université catholique de Louvain, CORE)

  • Jeroen V.K. Rombouts

    () (Institute of Applied Economics at HEC Montréal, CIRANO, CIRPEE, and CORE)

Abstract

GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. Flexible alternatives are Markov-switching GARCH and change-point GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issue is the computation of their marginal likelihood, which is essential for determining the number of regimes or change-points. We solve the problem by using particle MCMC, a technique proposed by Andrieu, Doucet, and Holenstein (2010). We examine the performance of this new method on simulated data, and we illustrate its use on several return series.

Suggested Citation

  • Luc Luc & Arnaud Dufays & Jeroen V.K. Rombouts, 2011. "Marginal Likelihood for Markov-switching and Change-point Garch Models," CREATES Research Papers 2011-41, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-41
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jin, Xin & Maheu, John M., 2016. "Modeling covariance breakdowns in multivariate GARCH," Journal of Econometrics, Elsevier, vol. 194(1), pages 1-23.
    2. Menelaos Karanasos & Alexandros Paraskevopoulos & Faek Menla Ali & Michail Karoglou & Stavroula Yfanti, 2014. "Modelling Returns and Volatilities During Financial Crises: a Time Varying Coefficient Approach," Papers 1403.7179, arXiv.org.
    3. Arnaud Dufays & Maciej Augustyniak & Luc Bauwens, 2016. "A new approach to volatility modeling: the High-Dimensional Markov model," Cahiers de recherche 1609, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    4. Bauwens, Luc & Carpantier, Jean-François & Dufays, Arnaud, 2015. "Autoregressive moving average infinite hidden markov-switching models," CORE Discussion Papers 2015007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. Dufays, A. & Rombouts, V., 2015. "Sparse Change-Point Time Series Models," CORE Discussion Papers 2015032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
    8. repec:hal:journl:halshs-01339826 is not listed on IDEAS
    9. CARPANTIER, Jean-François & DUFAYS, Arnaud, 2014. "Specific Markov-switching behaviour for ARMA parameters," CORE Discussion Papers 2014014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. repec:taf:jnlbes:v:35:y:2017:i:2:p:162-182 is not listed on IDEAS
    11. Pappas, Vasileios & Ingham, Hilary & Izzeldin, Marwan & Steele, Gerry, 2016. "Will the crisis “tear us apart”? Evidence from the EU," International Review of Financial Analysis, Elsevier, vol. 46(C), pages 346-360.
    12. Nonejad, Nima, 2017. "Parameter instability, stochastic volatility and estimation based on simulated likelihood: Evidence from the crude oil market," Economic Modelling, Elsevier, vol. 61(C), pages 388-408.
    13. Arnaud Dufays, 2014. "On the conjugacy of off-line and on-line Sequential Monte Carlo Samplers," Working Paper Research 263, National Bank of Belgium.
    14. Monica Billio & Lorenzo Frattarolo & Hayette Gatfaoui & Philippe de Peretti, 2016. "Clustering in Dynamic Causal Networks as a Measure of Systemic Risk on the Euro Zone," Documents de travail du Centre d'Economie de la Sorbonne 16046r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Sep 2016.
    15. BAUWENS, Luc & DUFAYS, Arnaud & DE BACKER, Bruno, 2011. "Estimating and forecasting structural breaks in financial time series," CORE Discussion Papers 2011055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Karanasos, Menelaos & Paraskevopoulos, Alexandros G. & Menla Ali, Faek & Karoglou, Michail & Yfanti, Stavroula, 2014. "Modelling stock volatilities during financial crises: A time varying coefficient approach," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 113-128.
    17. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-33, March.
    18. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    20. Arnaud Dufays, 2015. "Evolutionary Sequential Monte Carlo Samplers for Change-point Models," Cahiers de recherche 1518, CIRPEE.
    21. repec:luc:wpaper:14-07 is not listed on IDEAS
    22. Arnaud Dufays, 2015. "Evolutionary Sequential Monte Carlo Samplers for Change-point Models," Cahiers de recherche 1508, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    23. 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".
    24. DUFAYS, Arnaud, 2012. "Infinite-state Markov-switching for dynamic volatility and correlation models," CORE Discussion Papers 2012043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Keywords

    Bayesian inference; Simulation; GARCH; Markov-switching model; Changepoint model; Marginal likelihood; Particle MCMC;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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