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

While 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 implementa...

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Bibliographic Details
Published inJournal of the American Statistical Association Vol. 117; no. 540; pp. 2147 - 2162
Main Authors Romano, Gaetano, Rigaill, Guillem, Runge, Vincent, Fearnhead, Paul
Format Journal Article
LanguageEnglish
Published Alexandria Taylor & Francis 02.10.2022
Taylor & Francis Ltd
Subjects
Algorithms
Autocorrelation
Bacteria
Bioinformatics
Breakpoints
Change detection
Changepoints
Changes
Computer Science
Dynamic programming
FPOP
Gene expression
Mathematics
Minimization
Noise
Optimal partitioning
Random walk
Regression analysis
Statistical methods
Statistics
Structural breaks
Structural breaks
Breakpoints
Optimal partitioning
FPOP
Dynamic programming
Changepoints
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Summary:While 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 minimizing a penalized cost based on this model. We develop a novel and efficient dynamic programming algorithm, DeCAFS, that can solve this minimization 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. Supplementary materials for this article are available online.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2021.1909598