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Application of modified information criterion to multiple change point problems

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  • Pan, Jianmin
  • Chen, Jiahua
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 10 (November)
    Pages: 2221-2241

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2221-2241

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    Related research

    Keywords: Consistency Convergence rate Limiting distribution Multiple change points Model complexity Regular parametric model;

    References

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    1. Lee, Chung-Bow, 1996. "Nonparametric multiple change-point estimators," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 295-304, May.
    2. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. David Siegmund, 2004. "Model selection in irregular problems: Applications to mapping quantitative trait loci," Biometrika, Biometrika Trust, vol. 91(4), pages 785-800, December.
    4. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    5. Lavielle, Marc, 1999. "Detection of multiple changes in a sequence of dependent variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 79-102, September.
    6. Ninomiya, Yoshiyuki, 2005. "Information criterion for Gaussian change-point model," Statistics & Probability Letters, Elsevier, vol. 72(3), pages 237-247, May.
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    Cited by:
    1. Anna Louise Schroeder & Piotr Fryzlewicz, 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. Ciuperca, Gabriela, 2011. "A general criterion to determine the number of change-points," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1267-1275, August.
    3. 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, vol. 23(2), pages 265-269, June.
    4. 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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