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Data segmentation for time series based on a general moving sum approach

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Abstract

We consider the multiple change point problem in a general framework based on estimating equations. This extends classical sample mean-based methodology to include robust methods but also different types of changes such as changes in linear regression or changes in count data including Poisson autoregressive time series. In this framework, we derive a general theory proving consistency for the number of change points and rates of convergence for the estimators of the locations of the change points. More precisely, two different types of MOSUM (moving sum) statistics are considered: A MOSUM-Wald statistic based on differences of local estimators and a MOSUM-score statistic based on a global inspection parameter. The latter is usually computationally less involved in particular in nonlinear problems where no closed form of the estimator is known such that numerical methods are required. Finally, we evaluate the methodology by some simulations as well as using geophysical well-log data.

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Notes

  1. Available at https://github.com/alan-turing-institute/rbocpdms/.

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Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 314838170, GRK 2297 MathCoRe. Claudia Kirch would also like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the program ’Statistical scalability’ when work on this paper was undertaken.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Mathematical Stochastics, Otto-von-Guericke University, Universitätsplatz 2, 39106, Magdeburg, Germany

    Claudia Kirch & Kerstin Reckruehm

  2. Center for Behavioral Brain Science (CBBS), Magdeburg, Germany

    Claudia Kirch

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  1. Claudia Kirch
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  2. Kerstin Reckruehm
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Correspondence to Claudia Kirch.

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Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s10463-023-00892-4. It contains additional simulations as well as the detailed proofs. Furthermore, R-code to generate Figs. 1, 2 and 3 is also provided.

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Kirch, C., Reckruehm, K. Data segmentation for time series based on a general moving sum approach. Ann Inst Stat Math 76, 393–421 (2024). https://doi.org/10.1007/s10463-023-00892-4

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