A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)

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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 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 M¨uller (2006), for a broad range of initial values and for heavy-tailed innovation densities. As such, they provide a useful complement to existing techniques.
Original languageEnglish
Place of PublicationTILBURG
PublisherFaculteit der Economische Wetenschappen
Number of pages36
Volume2011-002
Publication statusPublished - 2011

Publication series

NameCentER Discussion Paper
Volume2011-002

Fingerprint

Unit root tests
Distribution-free
Finite sample
Innovation
Sample size
Relative efficiency
Asymptotic optimality
Unit root
Dickey-Fuller test

Keywords

  • Unit root
  • Dickey-Fuller test
  • Local Asymptotic Normality
  • Rank test

Cite this

Hallin, M., van den Akker, R., & Werker, B. J. M. (2011). A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72). (CentER Discussion Paper; Vol. 2011-002). TILBURG: Faculteit der Economische Wetenschappen.
Hallin, M. ; van den Akker, R. ; Werker, B.J.M. / A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72). TILBURG : Faculteit der Economische Wetenschappen, 2011. (CentER Discussion Paper).
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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 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 M¨uller (2006), for a broad range of initial values and for heavy-tailed innovation densities. As such, they provide a useful complement to existing techniques.",
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Hallin, M, van den Akker, R & Werker, BJM 2011 'A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)' CentER Discussion Paper, vol. 2011-002, Faculteit der Economische Wetenschappen, TILBURG.

A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72). / Hallin, M.; van den Akker, R.; Werker, B.J.M.

TILBURG : Faculteit der Economische Wetenschappen, 2011. (CentER Discussion Paper; Vol. 2011-002).

Research output: Working paperDiscussion paperOther research output

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N2 - 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 M¨uller (2006), for a broad range of initial values and for heavy-tailed innovation densities. As such, they provide a useful complement to existing techniques.

AB - 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 M¨uller (2006), for a broad range of initial values and for heavy-tailed innovation densities. As such, they provide a useful complement to existing techniques.

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Hallin M, van den Akker R, Werker BJM. A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72). TILBURG: Faculteit der Economische Wetenschappen. 2011. (CentER Discussion Paper).