Spurious rejection using Dickey-Fuller tests

Abstract

In recent research Leybourne and co-workers examined the behaviour of the Dickey-Fuller τ test in the presence of structural breaks under the null. It was found that breaks in either level or drift occurring early in the sample period resulted in severe size distortion, with the unit root hypothesis spuriously rejected. Using Monte Carlo methods, the present letter analyses the finite-sample properties of the Dickey-Fuller K and τ tests. The results obtained show that in comparison to the τ test, the K test suffers far less size distortion in the presence of structural breaks under the null, dramatically so in the case of breaks in drift. The empirical analysis of Leybourne and co-workers is also revisited to further illustrate the contrasting behaviour of the two tests.