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

Marc Hallin, Ramon van den Akker and Bas Werker

No 2009_001, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

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 effciency, than the Dickey and Fuller test --except under Gaussian f, where they are doing equally well. Under Student t3 density f, the effciency 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 This gain is even larger in case the underlying f has fatter tails; under Cauchy f, where Dickey and Fuller is no longer valid, it can be considered infinite.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 e±cient 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 (search for similar items in EconPapers)
JEL-codes: C12 C22 (search for similar items in EconPapers)
Pages: 23 p.
Date: 2009
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published by:

Downloads: (external link)
https://dipot.ulb.ac.be/dspace/bitstream/2013/5411 ... _wpaper_2009_001.pdf RePEc_eca_wpaper_2009_001 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eca:wpaper:2009_001

Ordering information: This working paper can be ordered from
http://hdl.handle.ne ... ulb.ac.be:2013/54112

Access Statistics for this paper

More papers in Working Papers ECARES from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels ().