The present paper considers Dickey-Fuller-type unit root tests which account for a structural break occurring at an unknown point in time. The break is modelled by an innovational outlier approach. Provided that the break date is estimated correctly, the exact invariance to a mean and a slope...

The Perron test is the most commonly applied procedure to test for a unit root in the presence of a structural break of unknown timing in the trend function. Deriving the Perron-type test regression from an unobserved component model, it is shown that the test regression in fact is nonlinear in...