The effects of autocorrelation among errors on the consistency property of OLS variance estimator

In a linear regression model the ordinary least squares (OLS) variance estimator (S²) converges in probability to E(S²) even when the errors are autocorrelated. Of interest, however, is the rate of convergence. In this paper we shed some light on this question for the case of a linear trend model. In particular the relation between the rate of convergence and the correlation property of the errors is explored. It is shown that the retardation of the rate of convergence is not appreciable if the correlation is moderate, but it can be severe for extreme correlations.