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

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Author Info

  • 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. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(02), pages 256-271, August.
  2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  4. Haldrup, Neils, 1998. " An Econometric Analysis of I(2) Variables," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 595-650, December.
  5. 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.
  6. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Universite de Montreal, Departement de sciences economiques.
  7. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
  8. 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.
  9. Haldrup, Niels, 1994. "Semiparametric Tests for Double Unit Roots," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 109-22, January.
  10. Nabeya, S. & Perron, P., 1991. "Local Asymtotic Distributions Related to the AR(1) MOdel with Dependent Errors," Papers 362, Princeton, Department of Economics - Econometric Research Program.
  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. repec:att:wimass:9220 is not listed on IDEAS
  13. 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.
  14. 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.
  15. 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.
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Cited by:
  1. 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.
  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. Liu, Hui & Rodríguez, Gabriel, 2005. "Human activities and global warming: a cointegration analysis," MPRA Paper 9939, University Library of Munich, Germany.
  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 and Francis Journals, vol. 30(6), pages 635-667.
  5. Boriss Siliverstovs, . "The Bi-parameter Smooth Transition AutoRegressive model," Economics Working Papers 2000-16, School of Economics and Management, University of Aarhus.

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