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Consistency of Trend Break Point Estimator with Underspecified Break Number

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  • Jingjing Yang

    (Department of Economics, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV 89557, USA)

Abstract

This paper discusses the consistency of trend break point estimators when the number of breaks is underspecified. The consistency of break point estimators in a simple location model with level shifts has been well documented by researchers under various settings, including extensions such as allowing a time trend in the model. Despite the consistency of break point estimators of level shifts, there are few papers on the consistency of trend shift break point estimators in the presence of an underspecified break number. The simulation study and asymptotic analysis in this paper show that the trend shift break point estimator does not converge to the true break points when the break number is underspecified. In the case of two trend shifts, the inconsistency problem worsens if the magnitudes of the breaks are similar and the breaks are either both positive or both negative. The limiting distribution for the trend break point estimator is developed and closely approximates the finite sample performance.

Suggested Citation

  • Jingjing Yang, 2017. "Consistency of Trend Break Point Estimator with Underspecified Break Number," Econometrics, MDPI, vol. 5(1), pages 1-19, January.
    • Handle: RePEc:gam:jecnmx:v:5:y:2017:i:1:p:4-:d:86944
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    References listed on IDEAS

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    1. 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(4), pages 995-1029, August.
    2. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, September.
    3. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(3), pages 315-352, June.
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    5. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    6. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
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    8. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
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    Cited by:

    1. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    2. Emanuele Russo & Neil Foster-McGregor, 2022. "Characterizing growth instability: new evidence on unit roots and structural breaks in countries’ long run trajectories," Journal of Evolutionary Economics, Springer, vol. 32(2), pages 713-756, April.

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