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MCMC-based estimation of Markov Switching ARMA-GARCH models

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  • Jan Henneke
  • Svetlozar Rachev
  • Frank Fabozzi
  • Metodi Nikolov

Abstract

Regime switching models, especially Markov Switching (MS) models, are regarded as a promising way to capture nonlinearities in time series. Combining the elements of MS models with full Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroskedasticity (ARMA-GARCH) models poses severe difficulties for the computation of parameter estimators. Existing methods can become completely unfeasible due to the full path dependence of such models. In this article, we demonstrate how to overcome this problem. We formulate a full MS-ARMA-GARCH model and its Bayes estimator. This facilitates the use of Markov Chain Monte Carlo methods and allows us to develop an algorithm to compute the Bayes estimator of the regimes and parameters of our model. The approach is illustrated on simulated data and with returns from the New York Stock Exchange (NYSE). Our model is then compared to other approaches and clearly proves to be advantageous.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:applec:v:43:y:2011:i:3:p:259-271
    DOI: 10.1080/00036840802552379
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    Cited by:

    1. Luc Bauwens & Arie Preminger & Jeroen V. K. Rombouts, 2010. "Theory and inference for a Markov switching GARCH model," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 218-244, July.
    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. Bildirici, Melike E. & Sonustun, Bahri, 2021. "Chaotic behavior in gold, silver, copper and bitcoin prices," Resources Policy, Elsevier, vol. 74(C).
    5. 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.
    6. Cheng Peng & Young Shin Kim & Stefan Mittnik, 2022. "Portfolio Optimization on Multivariate Regime-Switching GARCH Model with Normal Tempered Stable Innovation," JRFM, MDPI, vol. 15(5), pages 1-23, May.
    7. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
    8. Jiang, Yu & Fang, Xianming, 2015. "Bull, bear or any other states in US stock market?," Economic Modelling, Elsevier, vol. 44(C), pages 54-58.
    9. 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".
    10. 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.
    11. DUFAYS, Arnaud, 2012. "Infinite-state Markov-switching for dynamic volatility and correlation models," LIDAM Discussion Papers CORE 2012043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Melike E. Bildirici & Memet Salman & Özgür Ömer Ersin, 2022. "Nonlinear Contagion and Causality Nexus between Oil, Gold, VIX Investor Sentiment, Exchange Rate and Stock Market Returns: The MS-GARCH Copula Causality Method," Mathematics, MDPI, vol. 10(21), pages 1-16, October.
    13. CARPANTIER, Jean-François & DUFAYS, Arnaud, 2014. "Specific Markov-switching behaviour for ARMA parameters," LIDAM Discussion Papers CORE 2014014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Hotta, Luiz Koodi & Trucíos Maza, Carlos César & Pereira, Pedro L. Valls & Zevallos Herencia, Mauricio Henrique, 2024. "Forecasting VaR and ES through Markov-switching GARCH models: does the specication matter?," Textos para discussão 567, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    15. Marcel Aloy & Gilles de Truchis & Gilles Dufrénot & Benjamin Keddad, 2013. "Shift-Volatility Transmission in East Asian Equity Markets," Working Papers halshs-00935364, HAL.
    16. Andrea Eross & Andrew Urquhart & Simon Wolfe, 2019. "Investigating risk contagion initiated by endogenous liquidity shocks: evidence from the US and eurozone interbank markets," The European Journal of Finance, Taylor & Francis Journals, vol. 25(1), pages 35-53, January.
    17. Shen, Zhiwei & Ritter, Matthias, 2016. "Forecasting volatility of wind power production," Applied Energy, Elsevier, vol. 176(C), pages 295-308.
    18. repec:ipg:wpaper:2014-500 is not listed on IDEAS
    19. 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.
    20. Maddalena Cavicchioli, 2021. "Statistical inference for mixture GARCH models with financial application," Computational Statistics, Springer, vol. 36(4), pages 2615-2642, December.
    21. Pierre-Julien Trombe & Pierre Pinson & Henrik Madsen, 2012. "A General Probabilistic Forecasting Framework for Offshore Wind Power Fluctuations," Energies, MDPI, vol. 5(3), pages 1-37, March.
    22. Yanlin Shi, 2023. "Long memory and regime switching in the stochastic volatility modelling," Annals of Operations Research, Springer, vol. 320(2), pages 999-1020, January.

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