Following Bierens (1997a,b) and Vogelsang (1998a,b), unit root tests can be constructed which are asymptotically invariant to parameters involved by the short run dynamics of the process. Such an approach is called nonparametric by Bierens (1997b) and can be used to test a wide range of nonlinear models. We consider three different versions of such a test. However, simulation results suggest that only the variance ratio statistic is able to compete with the traditional augmented Dickey-Fuller test. A straightforward generalization of the variance ratio statistic is suggested, which can be used to test the cointegration rank in the spirit of Johansen (1988).