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Leroux's method for general hidden Markov models

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  • Genon-Catalot, Valentine
  • Laredo, Catherine

Abstract

The method introduced by Leroux [Maximum likelihood estimation for hidden Markov models, Stochastic Process Appl. 40 (1992) 127-143] to study the exact likelihood of hidden Markov models is extended to the case where the state variable evolves in an open interval of the real line. Under rather minimal assumptions, we obtain the convergence of the normalized log-likelihood function to a limit that we identify at the true value of the parameter. The method is illustrated in full details on the Kalman filter model.

Suggested Citation

  • Genon-Catalot, Valentine & Laredo, Catherine, 2006. "Leroux's method for general hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 222-243, February.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:2:p:222-243
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Valentine Genon‐Catalot & Thierry Jeantheau & Catherine Laredo, 2003. "Conditional Likelihood Estimators for Hidden Markov Models and Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 297-316, June.
    3. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    4. Michael Sørensen, 2000. "Prediction-based estimating functions," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 123-147.
    5. Genon-Catalot, Valentine, 2003. "A non-linear explicit filter," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 145-154, January.
    6. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    7. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    8. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
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    Cited by:

    1. Douc, Randal & Olsson, Jimmy & Roueff, François, 2020. "Posterior consistency for partially observed Markov models," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 733-759.
    2. Benjamin Favetto & Adeline Samson, 2010. "Parameter Estimation for a Bidimensional Partially Observed Ornstein–Uhlenbeck Process with Biological Application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 200-220, June.

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