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Detecting linear trend changes in data sequences

Author

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  • Hyeyoung Maeng

    (Durham University)

  • Piotr Fryzlewicz

    (London School of Economics)

Abstract

We propose TrendSegment, a methodology for detecting multiple change-points corresponding to linear trend changes in one dimensional data. A core ingredient of TrendSegment is a new Tail-Greedy Unbalanced Wavelet transform: a conditionally orthonormal, bottom-up transformation of the data through an adaptively constructed unbalanced wavelet basis, which results in a sparse representation of the data. Due to its bottom-up nature, this multiscale decomposition focuses on local features in its early stages and on global features next which enables the detection of both long and short linear trend segments at once. To reduce the computational complexity, the proposed method merges multiple regions in a single pass over the data. We show the consistency of the estimated number and locations of change-points. The practicality of our approach is demonstrated through simulations and two real data examples, involving Iceland temperature data and sea ice extent of the Arctic and the Antarctic. Our methodology is implemented in the R package trendsegmentR, available from CRAN.

Suggested Citation

  • Hyeyoung Maeng & Piotr Fryzlewicz, 2024. "Detecting linear trend changes in data sequences," Statistical Papers, Springer, vol. 65(3), pages 1645-1675, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01458-5
    DOI: 10.1007/s00362-023-01458-5
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    References listed on IDEAS

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    1. Anastasiou, Andreas & Fryzlewicz, Piotr, 2022. "Detecting multiple generalized change-points by isolating single ones," LSE Research Online Documents on Economics 110258, London School of Economics and Political Science, LSE Library.
    2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    3. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    4. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
    5. Rafal Baranowski & Yining Chen & Piotr Fryzlewicz, 2019. "Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 649-672, July.
    6. Andreas Anastasiou & Piotr Fryzlewicz, 2022. "Detecting multiple generalized change-points by isolating single ones," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 141-174, February.
    7. Robbins, Michael W. & Lund, Robert B. & Gallagher, Colin M. & Lu, QiQi, 2011. "Changepoints in the North Atlantic Tropical Cyclone Record," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 89-99.
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