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A Partial Review on Testing for Change Points in Autoregressive Time Series Models

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Listed:
  • Mohamed Salah Eddine Arrouch

    (Chouaib Doukkali University)

  • Echarif Elharfaoui

    (Chouaib Doukkali University)

  • Mohamed-Amine Elaafani

    (Chouaib Doukkali University)

  • Sara Nejjam

    (Chouaib Doukkali University)

Abstract

This review discusses the detection of a single change-point in autoregressive models of order p. It begins by outlining parameter estimation. Subsequently, two common robust testing methods are considered: the Efficient Score Test (EST) and the Likelihood Ratio Test (LRT). The limiting distributions of the test statistics under the null hypothesis of no change, along with methods for pinpointing the location of the change-point, are presented. Both methods are backed by theoretical justifications. To illustrate the performance, a summary of a comprehensive simulation experiment under various change scenarios is included, confirming the convergence and performance of the discussed methods. Finally, an application of these techniques to real-world data, specifically analyzing changes in volatility is described. These findings are placed in context with recent algorithms in the literature, highlighting their comparative efficacy and reliability.

Suggested Citation

  • Mohamed Salah Eddine Arrouch & Echarif Elharfaoui & Mohamed-Amine Elaafani & Sara Nejjam, 2025. "A Partial Review on Testing for Change Points in Autoregressive Time Series Models," Methodology and Computing in Applied Probability, Springer, vol. 27(3), pages 1-35, September.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:3:d:10.1007_s11009-025-10185-3
    DOI: 10.1007/s11009-025-10185-3
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    References listed on IDEAS

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    1. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    2. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    3. 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.
    4. 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.
    5. 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.
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