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.