Efficient likelihood estimation in state space models

• 成果类型: Article
• 署名作者: Fuh, Cheng-Der
• 署名单位: Academia Sinica - Taiwan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000614
• 发表日期: 2006
• 页码: 2026-2068
• 关键词: hidden markov-models; dependent random vectors; asymptotic expansions; time-series; AUTOREGRESSIVE PROCESSES; renewal theory; normality; variance; Consistency; inference

摘要

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.