Reply to “On some problems in the article Efficient Likelihood Estimation in State Space Models” by Cheng-Der Fuh [Ann. Statist. 34 (2006) 2026–2068]
Year: 2010
Type: letter
Abstract: 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.
Source: The Annals of Statistics
DOI: 10.1214/09-aos748b
Author: Cheng-Der Fuh
Institutions: Aarhus University, National Central University, Academia Sinica
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W2017109259