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Detecting linear trend changes in data sequences

Maeng, Hyeyoung; Fryzlewicz, Piotr

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Authors

Piotr Fryzlewicz



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.

Citation

Maeng, H., & Fryzlewicz, P. (2023). Detecting linear trend changes in data sequences. Statistical Papers, https://doi.org/10.1007/s00362-023-01458-5

Journal Article Type Article
Acceptance Date May 22, 2023
Online Publication Date Jun 22, 2023
Publication Date 2023
Deposit Date Oct 16, 2023
Publicly Available Date Oct 16, 2023
Journal Statistical Papers
Print ISSN 0932-5026
Electronic ISSN 1613-9798
Publisher Springer
Peer Reviewed Peer Reviewed
DOI https://doi.org/10.1007/s00362-023-01458-5
Keywords Statistics, Probability and Uncertainty; Statistics and Probability
Public URL https://durham-repository.worktribe.com/output/1804030

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Licence
http://creativecommons.org/licenses/by/4.0/

Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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