Testing for a unit root when uncertain about the trend [Revised to become 07/03 above]

In this paper we consider the issue of testing for a unit root when it is uncertain as to whether or not a linear deterministic trend is present in the data. The Dickey-Fuller-type tests of Elliott, Rothenberg and Stock (1996), based on (local) GLS detrended (demeaned) data, are near asymptotically efficient when a deterministic trend is (is not) present in the data generating process. We consider a variety of strategies which aim to select the demeaned variant when a trend is not present and the detrended variant otherwise. Asymptotic and finite sample evidence demonstrates that some sophisticated strategies which involve auxiliary methods of trend detection are generally outperformed by a simple decision rule of rejecting the unit root null whenever either the GLS demeaned or GLS detrended Dickey-Fuller-type tests reject. We show that this simple strategy is asymptotically identical to a sequential testing strategy proposed by Ayat and Burridge (2000). Moreover, our results make it clear that any other unit root testing strategy, however elaborate, can at best only offer a rather modest improvement over the simple one.