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A Note on Quasi-Maximum-Likelihood Estimation in Hidden Markov Models with Covariate-Dependent Transition Probabilities

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  • Demian Pouzo
  • Zacharias Psaradakis
  • Martín Sola

Abstract

We consider hidden Markov models with a discrete-valued regime sequence whose transition probabilities are covariate-dependent. We show that consistent estimation of the parameters of the conditional distribution of the observable variables is possible via quasi-maximum-likelihood based on a (misspecified) mixture model without Markov dependence. Some related numerical results are also discussed.

Suggested Citation

  • Demian Pouzo & Zacharias Psaradakis & Martín Sola, 2023. "A Note on Quasi-Maximum-Likelihood Estimation in Hidden Markov Models with Covariate-Dependent Transition Probabilities," Department of Economics Working Papers 2023_01, Universidad Torcuato Di Tella.
    • Handle: RePEc:udt:wpecon:2023_01
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    References listed on IDEAS

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    1. Levine, David, 1983. "A remark on serial correlation in maximum likelihood," Journal of Econometrics, Elsevier, vol. 23(3), pages 337-342, December.
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    3. Engel, Charles & Hakkio, Craig S, 1996. "The Distribution of Exchange Rates in the EMS," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 1(1), pages 55-67, January.
    4. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
    5. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
    6. Bates, Charles & White, Halbert, 1985. "A Unified Theory of Consistent Estimation for Parametric Models," Econometric Theory, Cambridge University Press, vol. 1(2), pages 151-178, August.
    7. Demian Pouzo & Zacharias Psaradakis & Martin Sola, 2022. "Maximum Likelihood Estimation in Markov Regime‐Switching Models With Covariate‐Dependent Transition Probabilities," Econometrica, Econometric Society, vol. 90(4), pages 1681-1710, July.
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    More about this item

    Keywords

    Consistency; covariate-dependent transition probabilities; hidden Markov model; mixture model; quasi-maximum-likelihood; misspecified model.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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

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