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On the Robustness of Unit Root Tests in the Presence of Double Unit Roots

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  • Haldrup, Niels Prof.
  • Lildholdt, Peter

Abstract

We examine some of the consequences on commonly used unit root tests when the underlying series is integrated of order two rather than of order one. It turns out that standard augmented Dickey-Fuller type of tests for a single unit root have excessive density in the explosive region of the distribution. The lower (stationary) tail, however, will be virtually unaffected in the presence of double unit roots. On the other hand, the Phillips-Perron class of semi-parametric tests is shown to diverge to plus infinity asymptotically and thus favoring the explosive alternative. Numerical simulations are used to demonstrate the analytical results and some of the implications in finite samples.

Suggested Citation

  • Haldrup, Niels Prof. & Lildholdt, Peter, 2000. "On the Robustness of Unit Root Tests in the Presence of Double Unit Roots," University of California at San Diego, Economics Working Paper Series qt2k0780sh, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt2k0780sh
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    Cited by:

    1. Dean Fantazzini, 2020. "Short-term forecasting of the COVID-19 pandemic using Google Trends data: Evidence from 158 countries," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 59, pages 33-54.
    2. Bo Sandemann Rasmussen, "undated". "Government Debt and Capital Accumulation in the Blanchard-Cass-Yaari OLG Model," Economics Working Papers 2000-14, Department of Economics and Business Economics, Aarhus University.
    3. Nikolaj Malchow-Moeller & Bo Jellesmark Thorsen, "undated". "A Dynamic Agricultural Household Model with Uncertain Income and Irreversible and Indivisible Investments under Credit Constraints," Economics Working Papers 2000-7, Department of Economics and Business Economics, Aarhus University.
    4. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "A residual-based ADF test for stationary cointegration in I(2) settings," Journal of Econometrics, Elsevier, vol. 184(2), pages 280-294.
    5. Tomás Del Barrio Castro & Paulo M. M. Rodrigues & A. M. Robert Taylor, 2015. "On the Behaviour of Phillips–Perron Tests in the Presence of Persistent Cycles," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(4), pages 495-511, August.
    6. Fernando N. Oliveira, 2014. "The Market of Foreign Exchange Hedge in Brazil: Reaction of Financial Institutions to Interventions of the Central Bank," Economics Bulletin, AccessEcon, vol. 34(1), pages 174-187.
    7. K. D. Patterson & S. M. Heravi, 2003. "The impact of fat-tailed distributions on some leading unit roots tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(6), pages 635-667.
    8. Effrosyni Diamantoudi, 2003. "Equilibrium binding agreements under diverse behavioral assumptions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 431-446, September.
    9. Hui Liu & Gabriel Rodriguez, 2003. "Human Activities and Global Warming: A Cointegration Analysis," Working Papers 0307E, University of Ottawa, Department of Economics.
    10. Boriss Siliverstovs, 2005. "The Bi-parameter Smooth Transition Autoregressive model," Economics Bulletin, AccessEcon, vol. 3(23), pages 1-11.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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