Annals of Statistics

Gaussian Likelihood Estimation for Nearly Nonstationary AR(1) Processes

Dennis D. Cox

Abstract

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 $\infty$. 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.

Article information

Source
Ann. Statist., Volume 19, Number 3 (1991), 1129-1142.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348241

Digital Object Identifier
doi:10.1214/aos/1176348241

Mathematical Reviews number (MathSciNet)
MR1126317

Zentralblatt MATH identifier
0729.62077

JSTOR