Effect of Preliminary Unit Root Tests on Predictors for an Unknown Mean Gaussian AR(1) Process

Abstract

It is known from Diebold and Kilian [1] and Niwitpong [2] that a preliminary Dickey-Fuller unit root test [3] is useful for a one-step-ahead forecast of the trend of an AR(1) process and an unknown mean Gaussian AR(1) process respectively. In this paper, the more powerful preliminary unit root tests, based on the weighted symmetric estimator described  by Fuller [4], Pantula et al. [6] and Shin and So [5], are compared with Dickey-Fuller unit root test. Monte Carlo simulation results are given to compare the relative efficiencies of predictors using the scaled prediction mean squares error for an unknown mean AR(1) process after preliminary unit root tests.