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A class of simple distribution-free rank-based unit root tests

Marc Hallin (), Ramon van den Akker and Bas J.M. Werker

Journal of Econometrics, 2011, vol. 163, issue 2, 200-214

Abstract: 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 need 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 stressing asymptotic optimality, however, we emphasize finite-sample performances, which also depend, quite heavily, on initial values. It appears that our rank-based tests significantly outperform the traditional Dickey-Fuller tests, as well as the more recent procedures proposed by Elliott et al. (1996), Ng and Perron (2001), and Elliott and Müller (2006), for a broad range of initial values and for heavy-tailed innovation densities. Thus, they provide a useful complement to existing techniques.

Keywords: Unit; root; Dickey-Fuller; test; Local; asymptotic; normality; Rank; test (search for similar items in EconPapers)
Date: 2011
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