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The Phillips unit root tests for polynomials of integrated processes revisited

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  • Stypka, Oliver
  • Wagner, Martin

Abstract

We show that the Phillips (1987) unit root tests have nuisance parameter free limiting distributions when applied to polynomials of integrated processes driven by linear process errors. This substantially generalizes a similar result of Wagner (2012) allowing only for serially uncorrelated errors. The result is based on novel kernel weighted sum limit results involving powers of integrated processes. These results allow us to consider additional modifications of the Phillips (1987) tests applicable to polynomials of integrated processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecolet:v:176:y:2019:i:c:p:109-113
    DOI: 10.1016/j.econlet.2018.12.033
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    References listed on IDEAS

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    1. Wagner, Martin, 2012. "The Phillips unit root tests for polynomials of integrated processes," Economics Letters, Elsevier, vol. 114(3), pages 299-303.
    2. 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.
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    4. Stypka, Oliver & Wagner, Martin & Grabarczyk, Peter & Kawka, Rafael, 2017. "The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions," Economics Series 333, Institute for Advanced Studies.
    5. Zsolt Darvas, 2008. "Estimation Bias and Inference in Overlapping Autoregressions: Implications for the Target‐Zone Literature," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(1), pages 1-22, February.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Lars E. O. Svensson, 1992. "An Interpretation of Recent Research on Exchange Rate Target Zones," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 119-144, Fall.
    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Martin Wagner, 2015. "The Environmental Kuznets Curve, Cointegration and Nonlinearity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(6), pages 948-967, September.
    11. Wagner, Martin & Hong, Seung Hyun, 2016. "Cointegrating Polynomial Regressions: Fully Modified Ols Estimation And Inference," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1289-1315, October.
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    Cited by:

    1. Fabian Knorre & Martin Wagner & Maximilian Grupe, 2021. "Monitoring Cointegrating Polynomial Regressions: Theory and Application to the Environmental Kuznets Curves for Carbon and Sulfur Dioxide Emissions," Econometrics, MDPI, vol. 9(1), pages 1-35, March.
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