A Class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests

CentER Discussion Paper Series No. 2009-02

23 Pages Posted: 13 Jan 2009

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)

Date Written: January 9, 2009

Abstract

We propose a class of simple 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 by distribution-freeness, irrespective of the value of the drift and the actual underlying f. When based on a Gaussian reference density g, our tests (of the van der Waerden form) perform uniformly better, in terms of asymptotic relative efficiency, than the Dickey and Fuller test - except under Gaussian f, where they are doing equally well. Under Student t3 density f, the efficiency gain is as high as 110%, meaning that Dickey-Fuller requires over twice as many observations as we do in order to achieve comparable performance. This gain is even larger in case the underlying f has fatter tails; under Cauchy f, where Dickey and Fuller is no longer valid, it can be considered infinite. The test associated with reference density g is semiparametrically efficient when f happens to coincide with g, in the ubiquitous case that the model contains a non-zero drift. Finally, with an estimated density f(n)) substituted for the reference density g, our tests achieve uniform (with respect to f) semiparametric efficiency.

Keywords: Dickey-Fuller test, Local Asymptotic Normality

JEL Classification: C12, C22

Suggested Citation

Hallin, Marc and Van den Akker, Ramon and Werker, Bas J.M., A Class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests (January 9, 2009). CentER Discussion Paper Series No. 2009-02. Available at SSRN: https://ssrn.com/abstract=1326295 or http://dx.doi.org/10.2139/ssrn.1326295

Marc Hallin (Contact Author)

ECARES, Universite Libre de Bruxelles ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium
+32 2 650 5886 (Phone)
+32 2 650 5899 (Fax)

Ramon Van den Akker

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

K-623
PO Box 90153
Tilburg, 5000 LE
Netherlands

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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