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

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Pages (from-to)200-214
JournalJournal of Econometrics
Volume163
Issue number2
Publication statusPublished - 2011

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

@article{4d69bad9355c48619344295f9ea8ecd7,
title = "A class of simple distribution-free rank-based unit root tests",
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 M{\"u}ller (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",
author = "M. Hallin and {van den Akker}, R. and B.J.M. Werker",
note = "Appeared earlier as CentER Discussion Paper 2011-002",
year = "2011",
language = "English",
volume = "163",
pages = "200--214",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "2",

}

A class of simple distribution-free rank-based unit root tests. / Hallin, M.; van den Akker, R.; Werker, B.J.M.

In: Journal of Econometrics, Vol. 163, No. 2, 2011, p. 200-214.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - A class of simple distribution-free rank-based unit root tests

AU - Hallin, M.

AU - van den Akker, R.

AU - Werker, B.J.M.

N1 - Appeared earlier as CentER Discussion Paper 2011-002

PY - 2011

Y1 - 2011

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 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.

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 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.

KW - unit root

KW - Dickey-Fuller test

KW - local asymptotic normality

KW - rank test

M3 - Article

VL - 163

SP - 200

EP - 214

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 2

ER -