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A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS

Published online by Cambridge University Press:  12 November 2012

Timothy J. Vogelsang  and
Martin Wagner
Timothy J. Vogelsang*
Affiliation:
Michigan State University
Martin Wagner
Affiliation:
Institute for Advanced Studies, Vienna and Frisch Centre for Economic Research, Oslo
*
*Address correspondence to Timothy J. Vogelsang, Dept. of Economics, 486 W. Circle Drive, 110 Marshall-Adams Hall, East Lansing, MI 48224-1038; e-mail: [email protected].
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Abstract

In this paper we extend fixed-b asymptotic theory to the nonparametric Phillips–Perron (PP) unit root tests. We show that the fixed-b limits depend on nuisance parameters in a complicated way. These nonpivotal limits provide an alternative theoretical explanation for the well-known finite-sample problems of the PP tests. We also show that the fixed-b limits depend on whether deterministic trends are removed using one-step or two-step detrending approaches. This is in contrast to the asymptotic equivalence of the one- and two-step approaches under a consistency approximation for the long-run variance estimator. Based on these results we introduce modified PP tests that allow for asymptotically pivotal fixed-b inference. The theoretical analysis is cast in the framework of near-integrated processes, which allows us to study the asymptotic behavior both under the unit root null hypothesis and for local alternatives. The performance of the original and modified PP tests is compared by means of local asymptotic power and a small finite-sample simulation study.

Type
Miscellanea
Information
Econometric Theory , Volume 29 , Issue 3 , June 2013 , pp. 609 - 628
Copyright
Copyright © Cambridge University Press 2012 

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Footnotes

The authors thank a co-editor (A.M. Robert Taylor), two referees, conference participants at the DAGStat 2010 meeting in Dortmund, the 5th CSDA International Conference on Computational and Financial Econometrics in London, and seminar participants at the Institute for Advanced Studies in Vienna for helpful comments and suggestions. The authors acknowledge financial support from the Jubiläumsfonds of the Oesterreichische Nationalbank (grant 13398). The usual disclaimer applies.

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