TY  - BOOK
AU  - Vogelsang,Timothy J.
AU  - Wagner,Martin
TI  - A fixed-b perspective on the Phillips-Perron unit root tests
SN  - 02664666
AV  - HB139.T52 ECO 
PY  - 2013///
CY  - Cambridge
PB  - Cambridge University Press
KW  - nonparametric kernel estimator
KW  - long run variance
KW  - detrending
N2  - 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
UR  - https://doi.org/10.1017/S0266466612000485
ER  -