Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis

Abstract

Seemingly absent from the arsenal of currently available “nearly efficient” testing procedures for the unit root hypothesis, that is, tests whose asymptotic local power functions are virtually indistinguishable from the Gaussian power envelope, is a test admitting a (quasi-)likelihood ratio interpretation. We study the large sample properties of a quasi-likelihood ratio unit root test based on a Gaussian likelihood and show that this test is nearly efficient.