Rank tests for unit roots

In order to obtain exact distributional results without imposing restrictive parametric assumptions, several rank counterparts of the Dickey-Fuller statistic are considered. In particular, a rank counterpart of the score statistic is suggested which appears to have attractive theoretical properties. Assuming i.i.d. errors, an exact test is obtained for a random walk model with drift and under assumptions similar to Phillips & Perron (1988) the test is asymptotically valid. In a Monte Carlo study the rank tests are compared with their parametric counterparts.