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An infimum coefficient unit root test allowing for an unknown break in trend


  • Harvey, David I.
  • Leybourne, Stephen J.


In this paper we consider testing for a unit root in the possible presence of a trend break at an unknown time. Zivot and Andrews (1992) [Journal of Business and Economic Statistics 10, 251–270] proposed using the infimum of t-ratio Dickey–Fuller statistics across all candidate break points in a trimmed range, however this procedure can have an asymptotic size of one when a break occurs under the unit root null. We show that if the same approach is used, but instead with coefficient Dickey–Fuller statistics in an additive outlier framework, the test is asymptotically conservative when a break is present under the null, provided the degree of trimming is appropriately controlled. The test is also shown to have superior local asymptotic power to the t-ratio version.

Suggested Citation

  • Harvey, David I. & Leybourne, Stephen J., 2012. "An infimum coefficient unit root test allowing for an unknown break in trend," Economics Letters, Elsevier, vol. 117(1), pages 298-302.
  • Handle: RePEc:eee:ecolet:v:117:y:2012:i:1:p:298-302 DOI: 10.1016/j.econlet.2012.05.023

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    References listed on IDEAS

    1. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    2. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    3. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    4. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
    5. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    6. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    7. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    8. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
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    Cited by:

    1. David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, 2014. "Unit Root Testing under a Local Break in Trend using Partial Information on the Break Date," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(1), pages 93-111, February.

    More about this item


    Unit root test; Trend break; Minimum Dickey–Fuller test;

    JEL classification:

    • 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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