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Confidence sets for the date of a break in level and trend when the order of integration is unknown

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  • David Harvey
  • Stephen Leybourne

Abstract

We propose methods for constructing confidence sets for the timing of a break in level and/or trend that have asymptotically correct coverage for both I(0) and I(1) processes. These are based on inverting a sequence of tests for the break location, evaluated across all possible break dates. We separately derive locally best invariant tests for the I(0) and I(1) cases; under their respective assumptions, the resulting confidence sets provide correct asymptotic coverage regardless of the magnitude of the break. We suggest use of a pre-test procedure to select between the I(0)- and I(1)- based confidence sets, and Monte Carlo evidence demonstrates that our recommended procedure achieves good finite sample properties in terms of coverage and length across both I(0) and I(1) environments. An application using US macroeconomic data is provided which further evinces the value of these procedures.

Suggested Citation

  • David Harvey & Stephen Leybourne, 2014. "Confidence sets for the date of a break in level and trend when the order of integration is unknown," Discussion Papers 14/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:14/04
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    5. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2010. "Robust methods for detecting multiple level breaks in autocorrelated time series," Journal of Econometrics, Elsevier, vol. 157(2), pages 342-358, August.
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    17. Sayginsoy, Özgen & Vogelsang, Timothy J., 2011. "Testing For A Shift In Trend At An Unknown Date: A Fixed-B Analysis Of Heteroskedasticity Autocorrelation Robust Ols-Based Tests," Econometric Theory, Cambridge University Press, vol. 27(5), pages 992-1025, October.
    18. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2013. "Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics," Journal of Econometrics, Elsevier, vol. 177(2), pages 265-284.
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    Cited by:

    1. Harvey, David I. & Leybourne, Stephen J., 2016. "Improving the length of confidence sets for the date of a break in level and trend when the order of integration is unknown," Economics Letters, Elsevier, vol. 145(C), pages 239-245.
    2. 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.
    3. Bobenrieth, Eugenio S. & Bobenrieth, Juan R.A. & Wright, Brian D. & Guerra, Ernesto A., 2022. "A Weak Latent Trend Hides Strong Price Predictability: An Empirical Method For An Unrecognized Problem," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322210, Agricultural and Applied Economics Association.
    4. Eiji Kurozumi & Anton Skrobotov, 2018. "Confidence Sets for the Break Date in Cointegrating Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(3), pages 514-535, June.
    5. Yicong Lin & Mingxuan Song, 2023. "Robust bootstrap inference for linear time-varying coefficient models: Some Monte Carlo evidence," Tinbergen Institute Discussion Papers 23-049/III, Tinbergen Institute.

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    More about this item

    Keywords

    Level break; Trend break; Stationary; Unit root; Locally best invariant test; confidence sets;
    All these keywords.

    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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