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

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  • Vogelsang, Timothy J.
  • Wagner, Martin

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.

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  • Vogelsang, Timothy J. & Wagner, Martin, 2013. "A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS," Econometric Theory, Cambridge University Press, vol. 29(3), pages 609-628, June.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:03:p:609-628_00
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    References listed on IDEAS

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    1. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    2. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    3. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 435-463.
    4. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    5. Perron, Pierre & Vogelsang, Timothy J, 1992. "Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 467-470, October.
    6. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    7. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
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    Cited by:

    1. Hanck, Christoph & Demetrescu, Matei & Kruse, Robinson, 2015. "Fixed-b Asymptotics for t-Statistics in the Presence of Time-Varying Volatility," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112916, Verein für Socialpolitik / German Economic Association.
    2. Pedroni, Peter L. & Vogelsang, Timothy J. & Wagner, Martin & Westerlund, Joakim, 2015. "Nonparametric rank tests for non-stationary panels," Journal of Econometrics, Elsevier, vol. 185(2), pages 378-391.
    3. Demetrescu, Matei & Kruse, Robinson, 2015. "Testing heteroskedastic time series for normality," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113221, Verein für Socialpolitik / German Economic Association.
    4. Ahmed, Muhammad Ashfaq & Nawaz, Nasreen, 2023. "A Sufficient Statistical Test for Dynamic Stability," MPRA Paper 116684, University Library of Munich, Germany.
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    8. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    9. Stypka, Oliver & Wagner, Martin, 2019. "The Phillips unit root tests for polynomials of integrated processes revisited," Economics Letters, Elsevier, vol. 176(C), pages 109-113.
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    12. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    13. Wagner, Martin & Grabarczyk, Peter & Hong, Seung Hyun, 2020. "Fully modified OLS estimation and inference for seemingly unrelated cointegrating polynomial regressions and the environmental Kuznets curve for carbon dioxide emissions," Journal of Econometrics, Elsevier, vol. 214(1), pages 216-255.
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    More about this item

    JEL classification:

    • 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; State Space Models

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