Rank tests of unit root hypothesis with infinite variance errors

We consider a family of rank tests based on the regression rank score process introduced by Gutenbrunner and Jurečková (Ann. Statist. 20 (1992) 305) to test the unit root hypothesis under infinite variance innovations. Unlike the finite variance case as studied by Hasan and Koenker (Econometrica 65 (1997) 133) the original rankscore test statistics (Tn) exhibit a simple Gaussian limiting behavior. However, finite sample investigations suggest a correction similar to what HK proposed. This corrected version (ŜT) has reliable size, and exhibits remarkable power even in near unit root cases under a variety of α-stable distributions. Also, the test statistics do not depend on the α parameter.