A Class of Simple Distribution-Free Rank-Based Unit Root Tests

CentER Discussion Paper Series No. 2011-002 (Revision of 2009-02, 2010-72)

36 Pages Posted: 23 Jan 2011

See all articles by Marc Hallin

Marc Hallin

ECARES, Universite Libre de Bruxelles

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

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Date Written: January 20, 2011

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 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 finitesample performances. Finite-sample performances of unit root tests, however, depend quite heavily on initial values. We therefore investigate those performances as a function of 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 Muller (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: Unit root, Dickey-Fuller test, Local Asymptotic Normality, Rank test

JEL Classification: C12, C22.

Suggested Citation

Hallin, Marc and Van den Akker, Ramon and Werker, Bas J.M., A Class of Simple Distribution-Free Rank-Based Unit Root Tests (January 20, 2011). CentER Discussion Paper Series No. 2011-002 (Revision of 2009-02, 2010-72), Available at SSRN: https://ssrn.com/abstract=1744867 or http://dx.doi.org/10.2139/ssrn.1744867

Marc Hallin (Contact Author)

ECARES, Universite Libre de Bruxelles ( email )

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Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR ( email )

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HOME PAGE: http://sites.google.com/site/rvdnakker/

Bas J.M. Werker

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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