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

Author

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  • Niels Haldrup
  • Peter Lildholdt

    () (Department of Economics, University of Aarhus, Denmark)

Abstract

We examine some of the consequences on commonly used unit root tests when the underlying series is integrated of order two. 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 test is shown to diverge to plus infinity asymptotically and thus will favor the explosive alternative. Numerical simulations are used to demonstrate the analytical results and some of the implications in finite samples.

Suggested Citation

  • Niels Haldrup & Peter Lildholdt, "undated". "On the Robustness of Unit Root Tests in the Presence of Double Unit Roots," Economics Working Papers 2000-1, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:aarhec:2000-1
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    References listed on IDEAS

    as
    1. Dickey, David A & Pantula, Sastry G, 1987. "Determining the Ordering of Differencing in Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 455-461, October.
    2. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(02), pages 256-271, August.
    3. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
    4. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June.
    5. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
    6. Haldrup, Niels, 1994. "Semiparametric Tests for Double Unit Roots," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 109-122, January.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, pages 277-301.
    8. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. Haldrup, Niels, 1994. "The asymptotics of single-equation cointegration regressions with I(1) and I(2) variables," Journal of Econometrics, Elsevier, vol. 63(1), pages 153-181, July.
    11. Choi, In & Park, Joon Y. & Yu, Byungchul, 1997. "Canonical Cointegrating Regression and Testing for Cointegration in the Presence of I(1) and I(2) Variables," Econometric Theory, Cambridge University Press, vol. 13(06), pages 850-876, December.
    12. Niels Haldrup, 1998. "An Econometric Analysis of I(2) Variables," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 595-650, December.
    13. Shin, Dong Wan & Kim, Hyun Jung, 1999. "Semiparametric Tests for Double Unit Roots Based on Symmetric Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 67-73, January.
    14. Sen, D L & Dickey, David A, 1987. "Symmetric Test for Second Differencing in Univariate Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 463-473, October.
    15. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, pages 277-301.
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    Cited by:

    1. Hui Liu & Gabriel Rodriguez, 2003. "Human Activities and Global Warming: A Cointegration Analysis," Working Papers 0307E, University of Ottawa, Department of Economics.
    2. Boriss Siliverstovs, 2005. "The Bi-parameter Smooth Transition Autoregressive model," Economics Bulletin, AccessEcon, pages 1-11.
    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. 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.
    5. Roberto Chang & Andrés Velasco, 2000. "Liquidity Crises in Emerging Markets: Theory and Policy," NBER Chapters,in: NBER Macroeconomics Annual 1999, Volume 14, pages 11-78 National Bureau of Economic Research, Inc.
    6. 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.
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    8. Havas, Attila, 2007. "O alargamento da UE e a política de Inovação nos países da Europa Central: O caso da Hungria
      [EU enlargement and innovation policy in Central European countries: The case of Hungary]
      ," MPRA Paper 69874, University Library of Munich, Germany.
    9. Thomas Horvath & Peter Huber, 2013. "The impact of networks, segregation and diversity on migrants' labour market integration," WWWforEurope Working Papers series 22, WWWforEurope.
    10. Attila Havas, 2009. "ERAWATCH Country Report 2008 - An Assessment of Research System and Policies: Hungary," JRC Working Papers JRC50011, Joint Research Centre (Seville site).
    11. Havas, Attila, 2004. "EU Enlargement and Innovation Policy in Central European Countries: The case of Hungary," MPRA Paper 69872, University Library of Munich, Germany.
    12. Igor Fedotenkov, 2014. "Coordination of Pension Systems When Technologies are Different," CESifo Economic Studies, CESifo, vol. 60(1), pages 246-256.
    13. 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.

    More about this item

    Keywords

    Unit root tests; Phillips-Perron test; I(1) versus I(2);

    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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