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An Advanced Segmentation Approach to Piecewise Regression Models

Author

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  • Kang-Ping Lu

    (Department of Applied Statistics, National Taichung University of Science and Technology, Taichung 404336, Taiwan)

  • Shao-Tung Chang

    (Department of Mathematics, National Taiwan Normal University, Taipei 106308, Taiwan)

Abstract

Two problems concerning detecting change-points in linear regression models are considered. One involves discontinuous jumps in a regression model and the other involves regression lines connected at unknown places. Significant literature has been developed for estimating piecewise regression models because of their broad range of applications. The segmented (SEG) regression method with an R package has been employed by many researchers since it is easy to use, converges fast, and produces sufficient estimates. The SEG method allows for multiple change-points but is restricted to continuous models. Such a restriction really limits the practical applications of SEG when it comes to discontinuous jumps encountered in real change-point problems very often. In this paper, we propose a piecewise regression model, allowing for discontinuous jumps, connected lines, or the occurrences of jumps and connected change-points in a single model. The proposed segmentation approach can derive the estimates of jump points, connected change-points, and regression parameters simultaneously, allowing for multiple change-points. The initializations of the proposed algorithm and the decision on the number of segments are discussed. Experimental results and comparisons demonstrate the effectiveness and superiority of the proposed method. Several real examples from diverse areas illustrate the practicability of the new method.

Suggested Citation

  • Kang-Ping Lu & Shao-Tung Chang, 2023. "An Advanced Segmentation Approach to Piecewise Regression Models," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4959-:d:1300422
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    References listed on IDEAS

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    1. Klaus Frick & Axel Munk & Hannes Sieling, 2014. "Multiscale change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 495-580, June.
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    8. Vito Muggeo & Massimo Attanasio & Mariano Porcu, 2009. "A segmented regression model for event history data: an application to the fertility patterns in Italy," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(9), pages 973-988.
    9. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
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