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August 2006 Efficient likelihood estimation in state space models
Cheng-Der Fuh
Ann. Statist. 34(4): 2026-2068 (August 2006). DOI: 10.1214/009053606000000614


Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root for each n, then there is a consistent sequence of estimators of the unknown parameters. If, in addition, the supremum of the log likelihood function is integrable, the MLE exists and is strongly consistent. Edgeworth expansion of the approximate solution of likelihood equation is also established. Several examples, including Markov switching models, ARMA models, (G)ARCH models and stochastic volatility (SV) models, are given for illustration.


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Cheng-Der Fuh. "Efficient likelihood estimation in state space models." Ann. Statist. 34 (4) 2026 - 2068, August 2006.


Published: August 2006
First available in Project Euclid: 3 November 2006

zbMATH: 1246.62185
MathSciNet: MR2283726
Digital Object Identifier: 10.1214/009053606000000614

Primary: 62M09
Secondary: 62E25 , 62F12

Keywords: (G)ARCH models , ARMA models , asymptotic expansion , asymptotic normality , consistency , efficiency , incomplete data , iterated random functions , Markov switching models , maximum likelihood , stochastic volatility models

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 4 • August 2006
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