Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise. Issue 540 (2nd October 2022)

• Record Type: Journal Article
• Authors: Romano, Gaetano; Rigaill, Guillem; Runge, Vincent; Fearnhead, Paul
• Is Part Of: Journal of the American Statistical Association. Volume 117:Issue 540(2022)
• Page Start: 2147
• Page End: 2162
• Publication Date: 2022-10-02
• Subjects: Breakpoints -- Changepoints -- Dynamic programming -- FPOP -- Optimal partitioning -- Structural breaks; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2021.1909598
• Languages: English
• ISSNs: 0162-1459

Abstract

Abstract: 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.