On Small Sample Properties of the Wald,LR and LM Tests in a Linear Model with AR(1) Errors

When the error terms are autocorrelated, the conventional t-tests for individual regression coefficients mislead us to over-rejection of the null hypothesis. We examine, by Monte Carlo experiments, the small sample properties of the unrestricted estimator of ρ and of the estimator of ρ restricted by the null hypothesis. We compare the small sample properties of the Wald, likelihood ratio and Lagrange multiplier test statistics for individual regression coefficients. It is shown that when the null hypothesis is true, the unrestricted estimator of ρ is biased. It is also shown that the Lagrange multiplier test using the maximum likelihood estimator of ρ performs better than the Wald and likelihood ratio tests.