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

Research output: Contribution to journalArticlepeer-review


Colleges, School and Institutes

External organisations

  • Department of Economics, University of Ioannina
  • Department of Economics, Athens University of Economics and Business


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.


Original languageEnglish
Pages (from-to)54-59
Number of pages6
JournalStatistics and Probability Letters
Early online date11 Dec 2017
Publication statusPublished - 1 Apr 2018


  • AR(1) disturbances, Asymptotic approximations, Autocorrelation robust inference, Linear regression, Stochastic expansions