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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

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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.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2000-13.

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Date of creation: Jun 2000
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Handle: RePEc:cdl:ucsdec:2000-13

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Haldrup, Neils, 1998. " An Econometric Analysis of I(2) Variables," Journal of Economic Surveys, Blackwell Publishing, vol. 12(5), pages 595-650, December. [Downloadable!] (restricted)
  2. 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.
  3. 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.
  4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  6. 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.
  7. Haldrup, Niels, 1994. "Semiparametric Tests for Double Unit Roots," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 109-22, January.
  8. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Blackwell Publishing, vol. 63(3), pages 435-63, July. [Downloadable!] (restricted)
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  9. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Blackwell Publishing, vol. 61(4), pages 631-53, October. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
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  1. 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, January. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  3. 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. [Downloadable!]
  4. Liu, Hui & Rodríguez, Gabriel, 2005. "Human activities and global warming: a cointegration analysis," MPRA Paper 9939, University Library of Munich, Germany. [Downloadable!]
  5. Boriss Siliverstovs, . "The Bi-parameter Smooth Transition AutoRegressive model," Economics Working Papers 2000-16, School of Economics and Management, University of Aarhus. [Downloadable!]
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