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Testing for a break in trend when the order of integration is unknown

  • Iacone, Fabrizio
  • Leybourne, Stephen J.
  • Robert Taylor, A.M.

Harvey, Leybourne and Taylor [Harvey, D.I., Leybourne, S.J., Taylor, A.M.R. 2009. Simple, robust and powerful tests of the breaking trend hypothesis. Econometric Theory 25, 995–1029] develop a test for the presence of a broken linear trend at an unknown point in the sample whose size is asymptotically robust as to whether the (unknown) order of integration of the data is either zero or one. This test is not size controlled, however, when this order assumes fractional values; its asymptotic size can be either zero or one in such cases. In this paper we suggest a new test, based on a sup-Wald statistic, which is asymptotically size-robust across fractional values of the order of integration (including zero or one). We examine the asymptotic power of the test under a local trend break alternative. The finite sample properties of the test are also investigated.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 176 (2013)
Issue (Month): 1 ()
Pages: 30-45

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Handle: RePEc:eee:econom:v:176:y:2013:i:1:p:30-45
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  1. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  2. Karim M. Abadir & Walter Distaso & Liudas Giraitis, 2011. "An I() model with trend and cycles," Post-Print peer-00834425, HAL.
  3. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, vol. 130(2), pages 209-233, February.
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  8. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  9. repec:cep:stiecm:/2003/449 is not listed on IDEAS
  10. Katsumi Shimotsu, 2006. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Working Papers 1061, Queen's University, Department of Economics.
  11. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
  12. David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, . "Simple, Robust and Powerful Tests of the Breaking Trend Hypothesis," Discussion Papers 06/11, University of Nottingham, School of Economics.
  13. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
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