Behaviour of the standard and symmetric Dickey-Fuller-type tests when there is a break under the null hypothesis

We examine the behaviour of tests of the unit root null hypothesis when the true generating model is I (1) with a break. Asymptotic distributional results are derived predicting that the standard Dickey–Fuller test will in that case yield frequent rejections of the null for relatively early breaks. This phenomenon is most severe for lowest values of the break fraction under a break in level, and for a break in slope occurring about 15% of the way through the series. However, asymptotics predict that the phenomenon will not be present for a modified test based on a symmetric weighted estimator. The theoretical predictions are confirmed by simulation evidence.