A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS
AbstractWe 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.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 29 (2013)
Issue (Month): 03 (June)
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Other versions of this item:
- Vogelsang, Timothy J. & Wagner, Martin, 2011. "A Fixed-b Perspective on the Phillips-Perron Unit Root Tests," Economics Series 272, Institute for Advanced Studies.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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Journal of Time Series Analysis,
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- Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
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05-08, Cornell University, Center for Analytic Economics.
- Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
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- Vogelsang, Timothy J. & Wagner, Martin, 2014. "Integrated modified OLS estimation and fixed-b inference for cointegrating regressions," Journal of Econometrics, Elsevier, vol. 178(2), pages 741-760.
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