Revisiting simple linear regression with autocorrelated errors

This paper studies properties of ordinary and generalised least squares estimators in a simple linear regression with stationary autocorrelated errors. Explicit expressions for the variances of the regression parameter estimators are derived for some common time series autocorrelation structures, including a first-order autoregression and general moving averages. Applications of the results include confidence intervals and an example where the variance of the trend slope estimator does not increase with increasing autocorrelation. Copyright Biometrika Trust 2004, Oxford University Press.