Asymptotic expansions for the mean and variance of the serial correlation coefficient

Two models are considered for the estimation of the serial correlation coefficient α of a first-order auto-regressive Gaussian process. Series expansions are obtained for the first two moments of α^ 1 the least squares estimator for α. The series expansions are carried to terms of order T−3 and α4 (where T is the observed length of the series) thus extending the asymptotic results of several authors (e. g. Bartlett, 1946; Hurwicz, 1950; Kendall, 1954; Marriott & Pope, 1954).