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

Abstract

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.