Adjusted estimates and Wald statistics for the AR(1) model with constant

Adjusted profile likelihood of Cox and Reid (1993, Journal of the Royal Sta tistical Society B 55, 467-471) for the autoregressive coefficient of the A R(1) model with constant yields an estimator which can be more accurate tha n the maximum-likelihood estimator in small samples whether the process is stationary or a random walk, and in the latter case also asymptotically. A related estimator is asymptotically distributed compactly and symmetrically around zero under a random walk but is not consistent in general. The adju sted Wald statistic can follow the asymptotic standard normal distribution much better than the non-adjusted under stationarity or a drifted random wa lk. (C) 2000 Elsevier Science S.A. All rights reserved. JEL classification: C12; C13; C22.