Efficient likelihood estimation in state space models

Details Efficient likelihood estimation in state space models Efficient likelihood estimation in state space models

2006-11-13

arxiv.org/abs/math/0611376v3

Annals of Statistics 2006, Vol. 34, No. 4, 2026-2068

Mathematics

Statistics Theory

With the comments by Jens Ledet Jensen and reply to the comments. Published at http://dx.doi.org/10.1214/009053606000000614;

Scientific paper

10.1214/009053606000000614 10.12

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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