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

  • Luis C. Nunes

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

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Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 190.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:ausm04:190
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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. 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.
  3. 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 535-58, December.
  4. 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.
  5. 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(02), pages 359-368, February.
  6. Vogelsang, T.J. & Perron, P., 1994. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," Cahiers de recherche 9422, Universite de Montreal, Departement de sciences economiques.
  7. 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 559-75, 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. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  10. repec:cup:etheor:v:11:y:1995:i:2:p:359-68 is not listed on IDEAS
  11. 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 257-87, August.
  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 435-48, November.
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