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The Phillips unit root tests for polynomials of integrated processes

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  • Wagner, Martin

Abstract

In this paper, we derive the limiting distributions of the first order serial correlation coefficient and its t-statistic, which are the basis for the non-parametric unit root tests of Phillips (1987), for polynomials of integrated processes. The resulting limiting distributions depend upon nuisance parameters and in general the modification proposed by Phillips (1987), to achieve a nuisance parameter free limiting distribution, is not feasible for polynomials of integrated processes. For the special case of serially uncorrelated innovations, the limiting distributions are nuisance parameter free and are simulated. The distributions shift to the left with increasing variance for increasing polynomial orders.

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  • Wagner, Martin, 2012. "The Phillips unit root tests for polynomials of integrated processes," Economics Letters, Elsevier, vol. 114(3), pages 299-303.
    • Handle: RePEc:eee:ecolet:v:114:y:2012:i:3:p:299-303
    DOI: 10.1016/j.econlet.2011.11.006
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    References listed on IDEAS

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    1. Wagner, Martin, 2008. "The carbon Kuznets curve: A cloudy picture emitted by bad econometrics?," Resource and Energy Economics, Elsevier, vol. 30(3), pages 388-408, August.
    2. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(4), pages 888-947, August.
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    7. Bradford David F. & Fender Rebecca A & Shore Stephen H. & Wagner Martin, 2005. "The Environmental Kuznets Curve: Exploring a Fresh Specification," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 4(1), pages 1-28, June.
    8. 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.
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    10. Friedl, Birgit & Getzner, Michael, 2003. "Determinants of CO2 emissions in a small open economy," Ecological Economics, Elsevier, vol. 45(1), pages 133-148, April.
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    12. Hong, Seung Hyun & Wagner, Martin, 2011. "Cointegrating Polynomial Regressions," Economics Series 264, Institute for Advanced Studies.
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    Cited by:

    1. T. Daniel Coggin, 2023. "CO2, SO2 and economic growth: a cross-national panel study," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 47(2), pages 437-457, June.
    2. 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.
    3. 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.
    4. Suphi Sen & Bertrand Melenberg & Herman R. J. Vollebergh, 2016. "Identification and Estimation of the Environmental Kuznets Curve: Pairwise Differencing to Deal with Nonlinearity and Nonstationarity," CESifo Working Paper Series 5837, CESifo.
    5. 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.
    6. Martin Wagner, 2023. "Residual-based cointegration and non-cointegration tests for cointegrating polynomial regressions," Empirical Economics, Springer, vol. 65(1), pages 1-31, July.
    7. Daniel Ventosa-Santaulària & Carlos Vladimir Rodríguez-Caballero, 2013. "Polynomial Regressions and Nonsense Inference," Econometrics, MDPI, vol. 1(3), pages 1-13, November.

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