A study of the ' marginal' likelihood ratio test for serial correlation

Abstract

This is a study on the use of marginal likelihood for testing serial correlation in regression models. In particular, we consider a 'classical' model with first order autocorrelated errors and we investigate the possibility of improving the performance of the likelihood ratio test, in small samples, by using the marginal likelihood. This method allows us ti remove the effect of the presence of nuisance parameters in the likelihood function and to reduce the bias of the ML estimator of three autoregressive parameter, which seems to be the cause of the poor power of the likelihood ratio test. The distribution of the test statistic under the nullhypothesis, and its power under the alternatives, is thereby investigated.