Gaussian Likelihood Estimation for Nearly Nonstationary AR(1) Processes

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 than the other two, and that the conditional maximum likelihood estimator gives a very poor estimator of the process mean. Keywords: Likelihood estimation; Autoregressive processes; Nearly nonstationary time series; Ornstein Uhlenbeck process.