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Maximum likelihood estimation of the Markov-switching GARCH model

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  • Augustyniak, Maciej
Abstract
The Markov-switching GARCH model offers rich dynamics to model financial data. Estimating this path dependent model is a challenging task because exact computation of the likelihood is infeasible in practice. This difficulty led to estimation procedures either based on a simplification of the model or not dependent on the likelihood. There is no method available to obtain the maximum likelihood estimator without resorting to a modification of the model. A novel approach is developed based on both the Monte Carlo expectation–maximization algorithm and importance sampling to calculate the maximum likelihood estimator and asymptotic variance–covariance matrix of the Markov-switching GARCH model. Practical implementation of the proposed algorithm is discussed and its effectiveness is demonstrated in simulation and empirical studies.

Suggested Citation

  • Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    • Handle: RePEc:eee:csdana:v:76:y:2014:i:c:p:61-75
    DOI: 10.1016/j.csda.2013.01.026
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    8. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2018. "Indexed Markov Chains for financial data: testing for the number of states of the index process," Papers 1802.01540, arXiv.org.
    9. Maciej Augustyniak & Mathieu Boudreault & Manuel Morales, 2018. "Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 165-188, March.
    10. Wee, Damien C.H. & Chen, Feng & Dunsmuir, William T.M., 2022. "Likelihood inference for Markov switching GARCH(1,1) models using sequential Monte Carlo," Econometrics and Statistics, Elsevier, vol. 21(C), pages 50-68.
    11. Ardia, David & Bluteau, Keven & Boudt, Kris & Catania, Leopoldo, 2018. "Forecasting risk with Markov-switching GARCH models:A large-scale performance study," International Journal of Forecasting, Elsevier, vol. 34(4), pages 733-747.
    12. Kai Zheng & Yuying Li & Weidong Xu, 2021. "Regime switching model estimation: spectral clustering hidden Markov model," Annals of Operations Research, Springer, vol. 303(1), pages 297-319, August.
    13. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2018. "Markov switching GARCH models for Bayesian hedging on energy futures markets," Energy Economics, Elsevier, vol. 70(C), pages 545-562.
    14. Guglielmo D’Amico & Ada Lika & Filippo Petroni, 2019. "Change point dynamics for financial data: an indexed Markov chain approach," Annals of Finance, Springer, vol. 15(2), pages 247-266, June.
    15. Holzmann, Hajo & Schwaiger, Florian, 2016. "Testing for the number of states in hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 318-330.
    16. Li, Leon & Miu, Peter, 2023. "Are cryptocurrencies a safe haven for stock investors? A regime-switching approach," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 367-385.
    17. Herrera, Ana María & Hu, Liang & Pastor, Daniel, 2018. "Forecasting crude oil price volatility," International Journal of Forecasting, Elsevier, vol. 34(4), pages 622-635.
    18. Bauwens, Luc & De Backer, Bruno & Dufays, Arnaud, 2014. "A Bayesian method of change-point estimation with recurrent regimes: Application to GARCH models," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 207-229.
    19. Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.
    20. 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.
    21. BenSaïda, Ahmed, 2015. "The frequency of regime switching in financial market volatility," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 63-79.

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