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LM-Type tests for a Unit Root Allowing for a Break in Trend

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  • Luis C. Nunes

Abstract

We consider LM-type tests for a unit root allowing for a break in trend at an unknown date. In addition to the minimum LM test statistic, we propose new LM-type tests based on the least squares estimator of the break date under the null. We examine asymptotic behavior under the null hypothesis with and without a break. For all the endogenous break tests considered, the limiting distribution when there is a break in slope is not the same as when there is no break. Other authors have obtained similar results in the context of DF-type tests. Since this discrepancy is smaller for the LM-type based on the least squares estimator, smaller size distortions are to be expected when using this test statistic. Simulation experiments confirm the superiority in terms of size, power and break date estimation of the proposed method

Suggested Citation

  • Luis C. Nunes, 2004. "LM-Type tests for a Unit Root Allowing for a Break in Trend," Econometric Society 2004 Australasian Meetings 190, Econometric Society.
    • Handle: RePEc:ecm:ausm04:190
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    References listed on IDEAS

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    1. Junsoo Lee & Mark C. Strazicich, 2013. "Minimum LM unit root test with one structural break," Economics Bulletin, AccessEcon, vol. 33(4), pages 2483-2492.
    2. 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.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. 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.
    5. repec:bla:obuest:v:63:y:2001:i:5:p:535-58 is not listed on IDEAS
    6. 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.
    7. 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.
    8. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    9. 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.
    10. repec:bla:obuest:v:63:y:2001:i:5:p:559-75 is not listed on IDEAS
    11. 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.
    12. 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.
    13. 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.
    14. repec:cup:etheor:v:11:y:1995:i:2:p:359-68 is not listed on IDEAS
    15. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    Cited by:

    1. Pui Sun Tam & University of Macau, 2006. "Breaking trend panel unit root tests," Computing in Economics and Finance 2006 341, Society for Computational Economics.
    2. Chou, Win Lin, 2007. "Performance of LM-type unit root tests with trend break: A bootstrap approach," Economics Letters, Elsevier, vol. 94(1), pages 76-82, January.
    3. Chou, Win Lin, 2007. "Explaining China's regional health expenditures using LM-type unit root tests," Journal of Health Economics, Elsevier, vol. 26(4), pages 682-698, July.

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    More about this item

    Keywords

    Unit Root; Structural Change; Lagrange Multiplier Test; Breaking Trend;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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