Open Access
September, 1991 Gaussian Likelihood Estimation for Nearly Nonstationary AR(1) Processes
Dennis D. Cox
Ann. Statist. 19(3): 1129-1142 (September, 1991). DOI: 10.1214/aos/1176348241


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.


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Dennis D. Cox. "Gaussian Likelihood Estimation for Nearly Nonstationary AR(1) Processes." Ann. Statist. 19 (3) 1129 - 1142, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0729.62077
MathSciNet: MR1126317
Digital Object Identifier: 10.1214/aos/1176348241

Keywords: autoregressive processes , Likelihood estimation , nearly nonstationary time series , Ornstein-Uhlenbeck process

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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