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Point Estimation of the Parameters of Piecewise Regression Models

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  • Douglas M. Hawkins

Abstract

Two methods of fitting piecewise multiple regression models are presented. One, based on dynamic programming, yields maximum‐likelihood estimators and is suitable for sequences of moderate length. A second, hierarchical, procedure yields approximations to the maximum‐likelihood estimators and is suitable for very long sequences of data. Both methods have computational requirements that are linear in the number of segments.

Suggested Citation

  • Douglas M. Hawkins, 1976. "Point Estimation of the Parameters of Piecewise Regression Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(1), pages 51-57, March.
    • Handle: RePEc:bla:jorssc:v:25:y:1976:i:1:p:51-57
    DOI: 10.2307/2346519
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    1. Watson, S.D. & Lomas, K.J. & Buswell, R.A., 2019. "Decarbonising domestic heating: What is the peak GB demand?," Energy Policy, Elsevier, vol. 126(C), pages 533-544.
    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. Lee, Chien-Chiang & Chen, Mei-Ping & Chang, Chi-Hung, 2013. "Dynamic relationships between industry returns and stock market returns," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 119-144.
    4. Alessandro Casini & Pierre Perron, "undated". "Generalized Laplace Inference in Multiple Change-Points Models," Boston University - Department of Economics - Working Papers Series WP2018-012, Boston University - Department of Economics.
    5. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    6. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2020. "Testing jointly for structural changes in the error variance and coefficients of a linear regression model," Quantitative Economics, Econometric Society, vol. 11(3), pages 1019-1057, July.
    7. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    8. Bucarey, Víctor & Labbé, Martine & Morales, Juan M. & Pineda, Salvador, 2021. "An exact dynamic programming approach to segmented isotonic regression," Omega, Elsevier, vol. 105(C).
    9. Pierre Perron & Yohei Yamamoto, 2008. "Estimating and Testing Multiple Structural Changes in Models with Endogenous Regressors," Boston University - Department of Economics - Working Papers Series wp2008-017, Boston University - Department of Economics.
    10. Pierre Perron & Yohei Yamamoto, 2015. "Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 119-144, January.
    11. Alessandro Casini & Pierre Perron, 2017. "Continuous Record Laplace-based Inference about the Break Date in Structural Change Models," Boston University - Department of Economics - Working Papers Series WP2018-011, Boston University - Department of Economics.
    12. 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.
    13. Moonsoo Park & Yanhong Jin & Alan Love, 2011. "Dynamic and contemporaneous causality in a supply chain: an application of the US beef industry," Applied Economics, Taylor & Francis Journals, vol. 43(30), pages 4785-4801.
    14. Tsai-Hung Fan & Hui-Jane Hsieh & Hsin-Hsian Lee, 2011. "A binary tree algorithm on change points detection," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(3), pages 599-608, April.
    15. Castro, Bruno M. & Lemes, Renan B. & Cesar, Jonatas & Hünemeier, Tábita & Leonardi, Florencia, 2018. "A model selection approach for multiple sequence segmentation and dimensionality reduction," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 319-330.

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