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Maximum-likelihood estimation for hidden Markov models

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  • Leroux, Brian G.
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    Abstract

    Hidden Markov models assume a sequence of random variables to be conditionally independent given a sequence of state variables which forms a Markov chain. Maximum-likelihood estimation for these models can be performed using the EM algorithm. In this paper the consistency of a sequence of maximum-likelihood estimators is proved. Also, the conclusion of the Shannon-McMillan-Breiman theorem on entropy convergence is established for hidden Markov models.

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    File URL: http://www.sciencedirect.com/science/article/B6V1B-45FCT2R-13/2/69172e7661467437336fcd418654fa1c
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 40 (1992)
    Issue (Month): 1 (February)
    Pages: 127-143

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    Handle: RePEc:eee:spapps:v:40:y:1992:i:1:p:127-143

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    Related research

    Keywords: Markov chain consistency subadditive ergodic theorem identifiability entropy Kullback-Leibler divergence Shannon-McMillan-Breiman theorem;

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    Cited by:
    1. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    2. Genon-Catalot, Valentine, 2003. "A non-linear explicit filter," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 145-154, January.
    3. Peiming Wang & Martin Puterman, 1999. "Markov Poisson regression models for discrete time series. Part 1: Methodology," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 855-869.
    4. Olsson, Jimmy & Rydén, Tobias, 2008. "Asymptotic properties of particle filter-based maximum likelihood estimators for state space models," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 649-680, April.
    5. Massimo Guidolin & Stuart Hyde, 2007. "What tames the Celtic tiger? portfolio implications from a multivariate Markov switching model," Working Papers 2006-029, Federal Reserve Bank of St. Louis.
    6. Massimo Guidolin & Sadayuki Ono, 2005. "Are the dynamic linkages between the macroeconomy and asset prices time-varying?," Working Papers 2005-056, Federal Reserve Bank of St. Louis.
    7. John Driffill & Turalay Kenc & Martin Sola & Fabio Spagnolo, 2008. "On Model Selection and Markov-Switching: An Empirical Examination of Term Structure Models with Regime Shifts," Department of Economics Working Papers 2008-04, Universidad Torcuato Di Tella.
    8. Mark, Brian L. & Ephraim, Yariv, 2013. "An EM algorithm for continuous-time bivariate Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 504-517.
    9. Massimo Guidolin & Stuart Hyde, 2008. "Equity portfolio diversification under time-varying predictability and comovements: evidence from Ireland, the US, and the UK," Working Papers 2008-005, Federal Reserve Bank of St. Louis.
    10. Hu, Shulan & Wu, Liming, 2011. "Large deviations for random dynamical systems and applications to hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 61-90, January.
    11. Turner, Rolf, 2008. "Direct maximization of the likelihood of a hidden Markov model," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4147-4160, May.
    12. Dannemann, Jorn & Holzmann, Hajo, 2008. "The likelihood ratio test for hidden Markov models in two-sample problems," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1850-1859, January.
    13. Armelle Guillou & Stéphane Loisel & Gilles Stupfler, 2011. "Estimation of the parameters of a Markov-modulated loss process in insurance," Working Papers hal-00589696, HAL.
    14. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
    15. Jörn Dannemann & Hajo Holzmann, 2008. "Likelihood Ratio Testing for Hidden Markov Models Under Non-standard Conditions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 35(2), pages 309-321.
    16. Rydén, Tobias, 1997. "On recursive estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 79-96, February.

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