---
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.'
author:
- |
    Gaetano Romano\
    Department of Mathematics and Statistics,\
    Lancaster University, Lancaster, UK\
     \
    Guillem Rigaill\
    Université Paris-Saclay, CNRS, INRAE, Univ Evry,\
    Institute of Plant Sciences Paris-Saclay (IPS2),\
    91405, Orsay, France\
     \
    Vincent Runge\
    Université Paris-Saclay, CNRS, Univ Evry,\
    Laboratoire de Mathématiques et Modélisation d’Evry\
    91037, Evry, France\
     \
    Paul Fearnhead\
    Department of Mathematics and Statistics,\
    Lancaster University, Lancaster, UK
bibliography:
- 'Bibliography.bib'
title: '**Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise**'
---

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[*Keywords:*]{} Breakpoints; Changepoints; Dynamic programming; FPOP; Optimal partitioning; Structural breaks.

[**Acknowledgements**]{} This work was supported by EPSRC grant EP/N031938/1, and an ATIGE grant from Genopole. The IPS2 benefits from the support of the LabEx Saclay Plant Sciences-SPS. We thank Pierre Nicolas for providing the output of hmmTiling on the *Bacillus subtilis* data and his R code allowing us to generate Figure \[fig:hmmtiling\], which closely resembles Figure 4 of [@nicolas2009transcriptional].
