Some Examples of Unit Root Tests

Abstract

It is not the intention in this chapter to provide a comprehensive review of unit root tests; that would be a task far more substantial than space allows. Rather, the idea is to introduce some tests that link in with developments in earlier chapters. Examples are given of two types of test: parametric and nonparametric. In the former case, probably the most frequently applied test is a version of the standard t test due to Dickey-Fuller (DF) tests, usually referred to as a τ test. This is a pseudo-t test in the sense that whilst it is constructed on the same general principle as at test, it does not have at distribution under the null hypothesis of a unit root. A closely related test is the coefficient or normalised bias test, referred to here as a δ test, which is just T times the numerator of the pseudo-t statistic. Whilst the 8 test is generally more powerful than the τ test, it is not so stable when the error process in the underlying model has a serially correlated structure, and is not so widely used as the τ test.