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Conditional Likelihood Estimators for Hidden Markov Models and Stochastic Volatility Models
Author(s) -
GeCatalot Valentine,
Jeantheau Thierry,
Laredo Catherine
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00332
Subject(s) - stochastic volatility , estimator , mathematics , contrast (vision) , markov chain , econometrics , hidden markov model , markov property , marginal likelihood , kalman filter , volatility (finance) , markov model , statistics , maximum likelihood , computer science , artificial intelligence
. 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.