GAUSSIAN LIKELIHOOD ESTIMATION FOR NEARLY NONSTATIONARY AR(1) PROCESSES

• 成果类型: Article
• 署名作者: COX, DD
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348241
• 发表日期: 1991
• 页码: 1129-1142
• 关键词: models

摘要

An asymptotic analysis is presented for estimation in the three-parameter first-order autoregressive model, where the parameters are the mean, autoregressive coefficient and variance of the shocks. The nearly nonstationary asymptotic model is considered wherein the autoregressive coefficient tends to 1 as sample size tends to infinity. Three different estimators are considered: the exact Gaussian maximum likelihood estimator, the conditional maximum likelihood or least squares estimator and some naive estimators. It is shown that the estimators converge in distribution to analogous estimators for a continuous-time Ornstein-Uhlenbeck process. Simulation results show that the MLE has smaller asymptotic mean squared error then the other two, and that the conditional maximum likelihood estimator gives a very poor estimator of the process mean.