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A Comparison of Alternative Asymptotic Frameworks to Analyze a Structural Change in a Linear Time Trend

Author

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  • Ai Deng

    (Department of Economics, Boston University)

  • Pierre Perron

    (Columbia Business School)

Abstract

This paper considers various asymptotic approximations to the finite sample distribution of the estimate of the break date in a simple one-break model for a linear trend function that exhibits a change in slope, with or without a concurrent change in intercept. The noise component is either stationary or has an autoregressive unit root. Our main focus is on comparing the so-called “bounded-trend” and “unbounded-trend” asymptotic frameworks. Not surprisingly, the “bounded-trend” asymptotic framework is of little use when the noise component is integrated. When the noise component is stationary, we obtain the following results. If the intercept does not change and is not allowed to change in the estimation, both frameworks yield the same approximation. However, when the intercept is allowed to change, whether or not it actually changes in the data, the “bounded-trend" asymptotic framework completely misses important features of the finite sample distribution of the estimate of the break date, especially the pronounced bimodality that was uncovered by Perron and Zhu (2005) and shown to be well captured using the “unbounded-trend” asymptotic framework. Simulation experiments confirm our theoretical findings, which expose the drawbacks of using the “bounded-trend” asymptotic framework in the context of structural change models.

Suggested Citation

  • Ai Deng & Pierre Perron, 2005. "A Comparison of Alternative Asymptotic Frameworks to Analyze a Structural Change in a Linear Time Trend," Boston University - Department of Economics - Working Papers Series WP2005-030, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2005-030
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    Cited by:

    1. Casini, Alessandro & Perron, Pierre, 2022. "Generalized Laplace Inference In Multiple Change-Points Models," Econometric Theory, Cambridge University Press, vol. 38(1), pages 35-65, February.
    2. Casini, Alessandro & Perron, Pierre, 2021. "Continuous record Laplace-based inference about the break date in structural change models," Journal of Econometrics, Elsevier, vol. 224(1), pages 3-21.
    3. Alessandro Casini, 2021. "Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models," Papers 2103.02981, arXiv.org.
    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. Md., Samsur Jaman, 2014. "Monitoring Structural Changes in NER: -An Empirical Analysis of Mizoram," MPRA Paper 60270, University Library of Munich, Germany.
    6. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    7. Brittle, Shane, 2009. "Ricardian Equivalence and the Efficacy of Fiscal Policy in Australia," Economics Working Papers wp09-10, School of Economics, University of Wollongong, NSW, Australia.
    8. Alessandro Casini & Taosong Deng & Pierre Perron, 2021. "Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference," Papers 2103.01604, arXiv.org, revised Nov 2021.
    9. Alessandro Casini & Pierre Perron, 2021. "Prewhitened Long-Run Variance Estimation Robust to Nonstationarity," Papers 2103.02235, arXiv.org, revised Dec 2021.
    10. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    11. Alessandro Casini & Pierre Perron, 2018. "Continuous Record Asymptotics for Change-Points Models," Papers 1803.10881, arXiv.org, revised Nov 2021.
    12. Alessandro Casini & Pierre Perron, 2015. "Continuous Record Asymptotics for Structural Change Models," Boston University - Department of Economics - Working Papers Series WP2018-010, Boston University - Department of Economics, revised Nov 2017.
    13. Federico Belotti & Alessandro Casini & Leopoldo Catania & Stefano Grassi & Pierre Perron, 2021. "Simultaneous Bandwidths Determination for DK-HAC Estimators and Long-Run Variance Estimation in Nonparametric Settings," Papers 2103.00060, arXiv.org.

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    Keywords

    change-point; confidence intervals; shrinking shifts; bounded trend; level shift.;
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