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Application of modified information criterion to multiple change point problems

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  • Pan, Jianmin
  • Chen, Jiahua

Abstract

The modified information criterion (MIC) is applied to detect multiple change points in a sequence of independent random variables. We find that the method is consistent in selecting the correct model, and the resulting test statistic has a simple limiting distribution. We show that the estimators for locations of change points achieve the best convergence rate, and their limiting distribution can be expressed as a function of a random walk. A simulation is conducted to demonstrate the usefulness of this method by comparing the powers between the MIC and the Schwarz information criterion.

Suggested Citation

  • Pan, Jianmin & Chen, Jiahua, 2006. "Application of modified information criterion to multiple change point problems," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2221-2241, November.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2221-2241
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    References listed on IDEAS

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    1. Schroeder, Anna Louise & Fryzlewicz, Piotr, 2013. "Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery," LSE Research Online Documents on Economics 54934, London School of Economics and Political Science, LSE Library.
    2. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    3. Lee Jaeeun & Chen Jie, 2019. "A penalized regression approach for DNA copy number study using the sequencing data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(4), pages 1-14, August.
    4. Liao, Guobo & Yin, Hongpeng & Chen, Min & Lin, Zheng, 2021. "Remaining useful life prediction for multi-phase deteriorating process based on Wiener process," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    5. A. Batsidis & N. Martín & L. Pardo & K. Zografos, 2016. "ϕ-Divergence Based Procedure for Parametric Change-Point Problems," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 21-35, March.
    6. Gordon J. Ross, 2020. "Tracking the evolution of literary style via Dirichlet–multinomial change point regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 149-167, January.
    7. Cai, Xia & Tian, Yubin & Ning, Wei, 2017. "Modified information approach for detecting change points in piecewise linear failure rate function," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 130-140.
    8. Marie Hušková & Zuzana Prášková, 2014. "Comments 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 265-269, June.
    9. 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.
    10. Ciuperca, Gabriela, 2011. "A general criterion to determine the number of change-points," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1267-1275, August.
    11. Wu, Y., 2008. "Simultaneous change point analysis and variable selection in a regression problem," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2154-2171, October.

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