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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 ()
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Ramon Van Den Akker: Tilburg University [Tilburg] - Netspar
Bas J.M. Werker: Tilburg University [Tilburg] - Netspar

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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 , which needs not coincide with the unknown actual innovation density . 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, which, quite heavily, also depend 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 Elliot, Rothenberg, and Stock (1996), Ng and Perron (2001), and Elliott and Müller (2006), for a broad range of initial values and for heavy-tailed innovation densities. As such, they provide a useful complement to existing techniques.

Keywords: C12; C22; Unit root; Dickey-Fuller test; Local asymptotic normality; Rank test (search for similar items in EconPapers)
Date: 2011-06-15
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Published in Econometrics, MDPI, 2011, ⟨10.1016/j.jeconom.2011.03.007⟩

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