Abstract
Exact mean and variance of the least squares estimate of the stationary first-order autoregressive coefficient, i.e., β in yt=α+βxt+ut are evaluated algebraically as well as numerically. It turns out that the least squares estimate is seriously biased for the sample of two-digits sizes typically dealt with in econometrics if the mean of the process is unknown, i.e., if the equation has a non-zero intercept (α≠0). Kendall's approximation to the mean and Barlett's approximation to the variance are shown to be fairly good. Also, our numerical results confirm Orcutt and Winokur's (Econometrica, Vol. 37) based on Monte Carlo experiments.
