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

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

Abstract

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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Bibliographic Info

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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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Trend break; Fractional integration; Sup-Wald statistic;

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References

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  1. 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.
  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. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
  4. Karim M. Abadir & Walter Distaso & Liudas Giraitis, 2011. "An I() model with trend and cycles," Post-Print peer-00834425, HAL.
  5. 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.
  6. Fabrizio Iacone & Peter M Robinson, 2004. "Cointegration in Fractional Systems with Deterministic Trends," STICERD - Econometrics Paper Series /2004/476, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  7. Peter M Robinson, 2004. "The Distance between Rival Nonstationary Fractional Processes," STICERD - Econometrics Paper Series /2004/468, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. Katsumi Shimotsu, 2002. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Economics Discussion Papers 543, University of Essex, Department of Economics.
  9. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  10. 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.
  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. 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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Cited by:
  1. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 23(2), pages 219-255, June.
  2. Bent Jesper Christensen & Robinson Kruse & Philipp Sibbertsen, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," CREATES Research Papers 2013-35, School of Economics and Management, University of Aarhus.

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