Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise

Romano, Gaetano and Rigaill, Guillem and Runge, Vincent and Fearnhead, Paul (2020) Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise. arXiv.

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Abstract

Whilst there are a plethora of algorithms for detecting changes in mean in univariate time-series, almost all struggle in real applications where there is autocorrelated noise or where the mean fluctuates locally between the abrupt changes that one wishes to detect. In these cases, default implementations, which are often based on assumptions of a constant mean between changes and independent noise, can lead to substantial over-estimation of the number of changes. We propose a principled approach to detect such abrupt changes that models local fluctuations as a random walk process and autocorrelated noise via an AR(1) process. We then estimate the number and location of changepoints by minimising a penalised cost based on this model. We develop a novel and efficient dynamic programming algorithm, DeCAFS, that can solve this minimisation problem; despite the additional challenge of dependence across segments, due to the autocorrelated noise, which makes existing algorithms inapplicable. Theory and empirical results show that our approach has greater power at detecting abrupt changes than existing approaches. We apply our method to measuring gene expression levels in bacteria.

Item Type:
Journal Article
Journal or Publication Title:
arXiv
Subjects:
ID Code:
148153
Deposited By:
Deposited On:
12 Oct 2020 15:10
Refereed?:
No
Published?:
Published
Last Modified:
31 Oct 2020 07:22