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

Author

Listed:
  • Claudia Kirch

    (Otto-von-Guericke University
    Center for Behavioral Brain Science (CBBS))

  • Kerstin Reckruehm

    (Otto-von-Guericke University)

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.

Suggested Citation

  • Claudia Kirch & Kerstin Reckruehm, 2024. "Data segmentation for time series based on a general moving sum approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(3), pages 393-421, June.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:3:d:10.1007_s10463-023-00892-4
    DOI: 10.1007/s10463-023-00892-4
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    References listed on IDEAS

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    1. Aggarwal, Reena & Inclan, Carla & Leal, Ricardo, 1999. "Volatility in Emerging Stock Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 33-55, March.
    2. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    3. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection—rejoinder," LSE Research Online Documents on Economics 106681, London School of Economics and Political Science, LSE Library.
    4. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection," LSE Research Online Documents on Economics 103430, London School of Economics and Political Science, LSE Library.
    5. Ruggieri, Eric & Antonellis, Marcus, 2016. "An exact approach to Bayesian sequential change point detection," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 71-86.
    6. Haeran Cho & Claudia Kirch, 2022. "Two-stage data segmentation permitting multiscale change points, heavy tails and dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 653-684, August.
    7. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.
    8. Chun Yip Yau & Zifeng Zhao, 2016. "Inference for multiple change points in time series via likelihood ratio scan statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 895-916, September.
    9. Paul Fearnhead & Peter Clifford, 2003. "On‐line inference for hidden Markov models via particle filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 887-899, November.
    10. Rafal Baranowski & Yining Chen & Piotr Fryzlewicz, 2019. "Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 649-672, July.
    11. Michael Messer, 2022. "Bivariate change point detection: Joint detection of changes in expectation and variance," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 886-916, June.
    12. Paul Fearnhead & Guillem Rigaill, 2019. "Changepoint Detection in the Presence of Outliers," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 169-183, January.
    13. Fryzlewicz, Piotr, 2023. "Narrowest Significance Pursuit: inference for multiple change-points in linear models," LSE Research Online Documents on Economics 118795, London School of Economics and Political Science, LSE Library.
    14. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    15. Lajos Horváth & Gregory Rice, 2014. "Rejoinder on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 287-290, June.
    16. Claudia Kirch & Joseph Tadjuidje Kamgaing, 2012. "Testing for parameter stability in nonlinear autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 365-385, May.
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