Robust multiscale estimation of time-average variance for time series segmentation
Robust multiscale estimation of time-average variance for time series segmentation
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often required in order to distinguish genuine changes from random fluctuations due to the noise. When serial dependence is present, using a single estimator of the noise level may not be appropriate. Instead, it is proposed to adopt a scale-dependent time-average variance constant that depends on the length of the data section in consideration, to gauge the level of the noise therein. Accordingly, an estimator that is robust to the presence of multiple mean shifts is developed. The consistency of the proposed estimator is shown under general assumptions permitting heavy-tailedness, and its use with two widely adopted data segmentation algorithms, the moving sum and the wild binary segmentation procedures, is discussed. The performance of the proposed estimator is illustrated through extensive simulation studies and on applications to the house price index and air quality data sets.
change point analysis, moving sum procedure, robust estimation, time-average variance constant, wild binary segmentation
McGonigle, Euan T.
1eec7a96-1343-4bf5-a131-432fe50842cd
Cho, Haeran
09d12733-9485-4092-b519-6ac6c9cb43ee
McGonigle, Euan T.
1eec7a96-1343-4bf5-a131-432fe50842cd
Cho, Haeran
09d12733-9485-4092-b519-6ac6c9cb43ee
McGonigle, Euan T. and Cho, Haeran
(2023)
Robust multiscale estimation of time-average variance for time series segmentation.
Computational Statistics & Data Analysis, 179, [107648].
(doi:10.1016/j.csda.2022.107648).
Abstract
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often required in order to distinguish genuine changes from random fluctuations due to the noise. When serial dependence is present, using a single estimator of the noise level may not be appropriate. Instead, it is proposed to adopt a scale-dependent time-average variance constant that depends on the length of the data section in consideration, to gauge the level of the noise therein. Accordingly, an estimator that is robust to the presence of multiple mean shifts is developed. The consistency of the proposed estimator is shown under general assumptions permitting heavy-tailedness, and its use with two widely adopted data segmentation algorithms, the moving sum and the wild binary segmentation procedures, is discussed. The performance of the proposed estimator is illustrated through extensive simulation studies and on applications to the house price index and air quality data sets.
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Accepted/In Press date: 17 October 2022
e-pub ahead of print date: 24 October 2023
Additional Information:
Funding Information:
Supported by Leverhulme Trust Research Project Grant RPG-2019-390.
Keywords:
change point analysis, moving sum procedure, robust estimation, time-average variance constant, wild binary segmentation
Identifiers
Local EPrints ID: 477550
URI: http://eprints.soton.ac.uk/id/eprint/477550
ISSN: 0167-9473
PURE UUID: 76d6c4e7-f49b-4066-a556-88ace1d2917e
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Date deposited: 08 Jun 2023 16:40
Last modified: 17 Mar 2024 04:20
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Contributors
Author:
Euan T. McGonigle
Author:
Haeran Cho
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