Identification of the true break date in innovational outlier unit root tests

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 shift holds for these tests under the null hypothesis. An erroneous estimation of the break date leads to considerable spurious rejections of the null hypothesis in small samples. In this paper, test procedures are developed using a components representation of the data generating process. In contrast to the conventionally used approaches, these tests enable the identification of the true break date and ensure the invariance property of the corresponding test statistics. Monte Carlo simulations of size and power testify the favorable properties of the developed tests.