A Class of Simple Distribution-Free Rank-Based Unit Root Tests
CentER Discussion Paper Series No. 2010-72 (revision of 2009-02)
26 Pages Posted: 30 Jul 2010
Date Written: June 30, 2010
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.
Keywords: Unit root, Dickey-Fuller test, Local Asymptotic Normality, Rank test
JEL Classification: C12, C22
Suggested Citation: Suggested Citation