This paper provides a new unit root test based on an alternative parameterization which has previously been considered by Bhargava (1986). This parameterization allows for trend under both the null and the alternative, without introducing any parameters that are irrelevant under either. This is not so in the Dickey-Fuller parameterizations. The new test is extracted from the score or LM principle under the assumption that the errors are iid N(0, sigma squared (epsilon)), but our asymptotics hold under more general assumptions about the errors. Two forms of the test (a coeﬀicient test and at t-test) are derived.
Phillips, Peter C.B. and Schmidt, Peter, "Testing for a Unit Root in the Presence of Deterministic Trends" (1989). Cowles Foundation Discussion Papers. 1176.