A Class of Simple Distribution-Free Rank-Based Unit Root Tests

We propose a class of distribution-free rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f . The validity of these tests, in terms of exact finite sample size, is guaranteed, irrespective of the actual underlying density, by distribution-freeness. Those tests are locally and asymptotically optimal under a particular asymptotic scheme, for which we provide a complete analysis of asymptotic relative efficiencies. Rather than asymptotic optimality, however, we emphasize finite-sample performances, and show that our rank-based tests perform significantly better than the traditional Dickey-Fuller tests. AMS 1980 subject classification : 62G10 and 62G20. JEL codes : C12, C22.