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

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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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2000-1.

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Length: 18
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Handle: RePEc:aah:aarhec:2000-1

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Web page: http://www.econ.au.dk/afn/

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

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References

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  1. repec:att:wimass:9220 is not listed on IDEAS
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  3. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. 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.
  5. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(02), pages 256-271, August.
  6. 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 455-61, October.
  7. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
  8. 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.
  9. 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.
  10. Niels Haldrup, 1998. "An Econometric Analysis of I(2) Variables," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 595-650, December.
  11. 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 463-73, October.
  12. Haldrup, Niels, 1994. "Semiparametric Tests for Double Unit Roots," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 109-22, January.
  13. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  14. 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.
  15. 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.
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Cited by:
  1. Boriss Siliverstovs, . "The Bi-parameter Smooth Transition AutoRegressive model," Economics Working Papers 2000-16, School of Economics and Management, University of Aarhus.
  2. Nikolaj Malchow-Moeller & Bo Jellesmark Thorsen, . "A Dynamic Agricultural Household Model with Uncertain Income and Irreversible and Indivisible Investments under Credit Constraints," Economics Working Papers 2000-7, School of Economics and Management, University of Aarhus.
  3. Andrés Rodríguez-Pose & Roberto Ezcurra, 2010. "Does decentralization matter for regional disparities? A cross-country analysis," Journal of Economic Geography, Oxford University Press, vol. 10(5), pages 619-644, September.
  4. 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.
  5. Hui Liu & Gabriel Rodriguez, 2003. "Human Activities and Global Warming: A Cointegration Analysis," Working Papers 0307E, University of Ottawa, Department of Economics.
  6. Bo Sandemann Rasmussen, . "Government Debt and Capital Accumulation in the Blanchard-Cass-Yaari OLG Model," Economics Working Papers 2000-14, School of Economics and Management, University of Aarhus.
  7. Roberto Chang & Andres Velasco, 1999. "Liquidity Crises in Emerging Markets: Theory and Policy," NBER Working Papers 7272, National Bureau of Economic Research, Inc.
  8. Thomas Horvath & Peter Huber, 2013. "The impact of networks, segregation and diversity on migrants' labour market integration," WWWforEurope Working Papers series 22, WWWforEurope.

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