Higher order expansions for error variance matrix estimates in the Gaussian AR(1) linear regression model

We derive a stochastic expansion of the error variance-covariance matrix estimator for the linear regression model under Gaussian AR(1) errors. The higher order accuracy terms of the refined formula are not directly derived from formal Edgeworth-type expansions but instead, the paper adopts Magadalinos' (1992) stochastic order of ω which is a convenient device to obtain the equivalent relation between the stochastic expansion and the asymptotic approximation of corresponding distribution functions. A Monte Carlo experiment compares tests based on the new estimator with others in the literature and shows that the new tests perform well.