Alternative size corrections for some GLS test statistics the case of the AR(1) model

Alternative size corrections are developed for the t and F tests in the AR(1) normal linear model. Edgeworth corrected critical values are obtained from normal, Student-t, chi-square, and F distributions. Alternatively, we may use Cornish-Fisher corrected test statistics to avoid the problem of negative tail ‘probabilities’ of an Edgeworth ‘distribution’. The use of the exact distributions (Student-t, F) results in approximations that are locally exact, i.e., they reduce to the exact formulae for a sufficient simplification of the model. Monte Carlo findings support the theoretical considerations in favour of the locally exact Cornish-Fisher corrections.