Behaviour of Dickey–Fuller Unit‐Root Tests Under Trend Misspecification

We analyse the case where a unit‐root test is based on a Dickey–Fuller regression the only deterministic term of which is a fixed intercept. Suppose, however, as could well be the case, that the actual data‐generating process includes a broken linear trend. It is shown theoretically, and verified empirically, that under the I (1) null and I (0) alternative hypotheses the Dickey–Fuller test can display a wide range of different characteristics depending on the nature and location of the break.