A Fixed-b Perspective on the Phillips-Perron Unit Root Tests

Timothy Vogelsang and Martin Wagner

No 272, Economics Series from Institute for Advanced Studies

Abstract: 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 non-pivotal limits provide an alternative theoretical explanation for the well known finite sample problems of PP tests. We also show that the fixed-b limits depend on whether deterministic trends are removed using one-step or two-step approaches, contrasting 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 fixed-b inference. The theoretical analysis is cast in the framework of near-integrated processes which allows to study the asymptotic behavior both under the unit root null hypothesis as well as for local alternatives. The performance of the original and modified tests is compared by means of local asymptotic power and a small simulation study.

Keywords: Nonparametric kernel estimator; long run variance; detrending; one-step; two-step (search for similar items in EconPapers)
JEL-codes: C12 C13 C32 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2011-07
New Economics Papers: this item is included in nep-ecm and nep-ets
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https://irihs.ihs.ac.at/id/eprint/2081 First version, 2011 (application/pdf)

Related works:
Journal Article: A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS (2013)
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