On the Asymptotic Power of Unit Root Tests

Closed forms for the distribution of some conventional statistics are given as a prelude to deriving their asymptotic power functions as unit root tests. In the process, an important distinction is drawn between two classes of statistics: one which relies on deterministic normalizations and the other which uses stochastic normalizations. When the data follow a driftless autoregression, a t test (which belongs to the second class) for a unit root is found to perform better than the other tests in small to moderate effective samples.