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

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  • Harvey, David I.
  • Leybourne, Stephen J.

Abstract

Harvey and Leybourne (2015) construct confidence sets for the timing of a break in level and/or trend, based on inverting sequences of test statistics for a break at all possible dates. These are valid, in the sense of yielding correct asymptotic coverage, for I(0) or I(1) errors. In constructing the tests, location-dependent weights are chosen for values of the break magnitude parameter such that each test conveniently has the same limit null distribution. By not imposing such a scheme, we show that it is generally possible to significantly shorten the length of the confidence sets, whilst maintaining accurate coverage properties.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecolet:v:145:y:2016:i:c:p:239-245
    DOI: 10.1016/j.econlet.2016.06.015
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    References listed on IDEAS

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    1. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    2. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
    3. David I. Harvey & Stephen J. Leybourne, 2014. "Break Date Estimation for Models with Deterministic Structural Change," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 623-642, October.
    4. Eiji Kurozumi & Yohei Yamamoto, 2015. "Confidence sets for the break date based on optimal tests," Econometrics Journal, Royal Economic Society, vol. 18(3), pages 412-435, October.
    5. Harvey, David I. & Leybourne, Stephen J., 2015. "Confidence sets for the date of a break in level and trend when the order of integration is unknown," Journal of Econometrics, Elsevier, vol. 184(2), pages 262-279.
    6. 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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    More about this item

    Keywords

    Level break; Trend break; Stationary; Unit root; 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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