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Minimum LM Unit Root Test with One Structural Break

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  • Junsoo Lee
  • Mark C. Strazicich

Abstract

In this paper, we propose a minimum LM unit root test that endogenously determines a structural break in intercept and trend. Critical values are provided, and size and power properties are compared to the endogenous one-break unit root test of Zivot and Andrews (1992). Nunes, Newbold, and Kuan (1997) and Lee and Strazicich (2001) previously demonstrated that the Zivot and Andrews test exhibits size distortions in the presence of a break under the null. In contrast, the one-break minimum LM unit root test exhibits no size distortions in the presence of a break under the null. As such, rejection of the null unambiguously implies a trend stationary process.

Suggested Citation

  • Junsoo Lee & Mark C. Strazicich, 2004. "Minimum LM Unit Root Test with One Structural Break," Working Papers 04-17, Department of Economics, Appalachian State University.
    • Handle: RePEc:apl:wpaper:04-17
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    References listed on IDEAS

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    1. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
    2. Uwe Hassler & Paulo M. M. Rodrigues, 2004. "Seasonal Unit Root Tests Under Structural Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 33-53, January.
    3. Luis C. Nunes & Paulo M. M. Rodrigues, 2011. "On LM‐type tests for seasonal unit roots in the presence of a break in trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 108-134, March.
    4. Lee, Junsoo & Strazicich, Mark C, 2001. "Break Point Estimation and Spurious Rejections with Endogenous Unit Root Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(5), pages 535-558, December.
    5. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    6. David I. Harvey & Stephen J. Leybourne & Paul Newbold, 2001. "Innovational Outlier Unit Root Tests With an Endogenously Determined Break in Level," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(5), pages 559-575, December.
    7. 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.
    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    9. 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.
    10. Amsler, Christine & Lee, Junsoo, 1995. "An LM Test for a Unit Root in the Presence of a Structural Change," Econometric Theory, Cambridge University Press, vol. 11(2), pages 359-368, February.
    11. 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.
    12. Nunes, Luis C & Newbold, Paul & Kuan, Chung-Ming, 1997. "Testing for Unit Roots with Breaks: Evidence on the Great Crash and the Unit Root Hypothesis Reconsidered," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(4), pages 435-448, November.
    13. repec:cup:etheor:v:11:y:1995:i:2:p:359-68 is not listed on IDEAS
    14. Junsoo Lee & Mark C. Strazicich, 2001. "Break Point Estimation and Spurious Rejections With Endogenous Unit Root Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(5), pages 535-558, December.
    15. Joseph P. Byrne & Roger Perman, 2006. "Unit Roots and Structural Breaks: A Survey of the Literature," Working Papers 2006_10, Business School - Economics, University of Glasgow.
    16. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-287, August.
    17. Harvey, David I & Leybourne, Stephen J & Newbold, Paul, 2001. "Innovational Outlier Unit Root Tests with an Endogenously Determined Break in Level," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(5), pages 559-575, December.
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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