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

Author

Listed:
  • 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.

Suggested Citation

  • Iacone, Fabrizio & Leybourne, Stephen J. & Robert Taylor, A.M., 2013. "Testing for a break in trend when the order of integration is unknown," Journal of Econometrics, Elsevier, vol. 176(1), pages 30-45.
  • Handle: RePEc:eee:econom:v:176:y:2013:i:1:p:30-45
    DOI: 10.1016/j.jeconom.2013.03.008
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    References listed on IDEAS

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    1. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2011. "An I(d) model with trend and cycles," Journal of Econometrics, Elsevier, vol. 163(2), pages 186-199, August.
    2. 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.
    3. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Simple, Robust, And Powerful Tests Of The Breaking Trend Hypothesis," Econometric Theory, Cambridge University Press, vol. 25(04), pages 995-1029, August.
    4. Robinson, P.M., 2005. "The distance between rival nonstationary fractional processes," Journal of Econometrics, Elsevier, vol. 128(2), pages 283-300, October.
    5. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
    6. Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation Of Fractional Integration With Unknown Mean And Time Trend," Econometric Theory, Cambridge University Press, vol. 26(02), pages 501-540, April.
    7. 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.
    8. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
    9. 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.
    10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    11. 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.
    12. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
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    Cited by:

    1. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2018. "A simple test on structural change in long-memory time series," Economics Letters, Elsevier, vol. 163(C), pages 90-94.
    2. Seong Yeon Chang & Pierre Perron, 2017. "Fractional Unit Root Tests Allowing for a Structural Change in Trend under Both the Null and Alternative Hypotheses," Econometrics, MDPI, Open Access Journal, vol. 5(1), pages 1-26, January.
    3. Iacone Fabrizio & Leybourne Stephen J. & Robert Taylor A.M., 2017. "Testing for a Change in Mean under Fractional Integration," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-8, January.
    4. Seong Yeon Chang & Pierre Perron, 2016. "Inference on a Structural Break in Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 555-574, July.
    5. 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, Department of Economics and Business Economics, Aarhus University.
    6. Jiawen Xu & Pierre Perron, 2013. "Robust testing of time trend and mean with unknown integration order errors Frequency (and Other) Contaminations," Boston University - Department of Economics - Working Papers Series 2013-006, Boston University - Department of Economics.
    7. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    8. 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;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.

    More about this item

    Keywords

    Trend break; Fractional integration; Sup-Wald statistic;

    JEL classification:

    • 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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