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Conditional Likelihood Estimators for Hidden Markov Models and Stochastic Volatility Models

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  • Valentine Genon‐Catalot
  • Thierry Jeantheau
  • Catherine Laredo

Abstract

ABSTRACT. This paper develops a new contrast process for parametric inference of general hidden Markov models, when the hidden chain has a non‐compact state space. This contrast is based on the conditional likelihood approach, often used for ARCH‐type models. We prove the strong consistency of the conditional likelihood estimators under appropriate conditions. The method is applied to the Kalman filter (for which this contrast and the exact likelihood lead to asymptotically equivalent estimators) and to the discretely observed stochastic volatility models.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:2:p:297-316
    DOI: 10.1111/1467-9469.00332
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    Cited by:

    1. 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.
    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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