Asymptotic Distribution of Maximum Likelihood Estimators in a Linear Model With Autoregressive Disturbances

Abstract

It is shown that maximum likelihood estimators of parameters of a linear model with autoregressive disturbances have an asymptotic multivariate normal distribution with mean vector equal to the true parameter values. Inspection of the variance matrix shows that the estimators are asymptotically efficient and that the estimates of coefficients of the independent variables have the same variance matrix as the best unbiased estimates for a modified model in which the autocorrelation parameter is known. It is conjectured that the asymptotic distribution of the estimates of coefficients of independent variables may be a useful approximation for moderate sized samples. Alternative approximations for the estimates of the autoregression coefficient and the variance are suggested for further study.*