The Order of the Error Term for Moments of the Log Likelihood Ratio Unit Root Test in an Autoregressive Process

This paper investigates the asymptotics of the log likelihood ratio test for a unit root in an autoregressive (AR) process of general order. The main result is that the expectation and variance (in fact, all moments) of the test statistic may, to the order of T-1, where T is the number of observations, be approximated by the expectation and variance of the corresponding test in an AR(1) process. This result has obvious implications for the asymptotics of unit root tests for panels. An explicit formula for the approximation error of a test in an AR(2) process is also given.