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Bootstrapping confidence intervals for the change-point of time series

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  • Marie Hušková
  • Claudia Kirch

Abstract

We study an at-most-one-change time-series model with an abrupt change in the mean and dependent errors that fulfil certain mixing conditions. We obtain confidence intervals for the unknown change-point via bootstrapping methods. Precisely, we use a block bootstrap of the estimated centred error sequence. Then, we reconstruct a sequence with a change in the mean using the same estimators as before. The difference between the change-point estimator of the resampled sequence and the one of the original sequence can be used as an approximation of the difference between the real change-point and its estimator. This enables us to construct confidence intervals using the empirical distribution of the resampled time series. A simulation study shows that the resampled confidence intervals are usually closer to their target levels and at the same time smaller than the asymptotic intervals. Copyright 2008 The Authors. Journal compilation 2008 Blackwell Publishing Ltd

Suggested Citation

  • Marie Hušková & Claudia Kirch, 2008. "Bootstrapping confidence intervals for the change-point of time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 947-972, November.
  • Handle: RePEc:bla:jtsera:v:29:y:2008:i:6:p:947-972
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    References listed on IDEAS

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    1. Antoch, Jaromír & Husková, Marie, 2001. "Permutation tests in change point analysis," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 37-46, May.
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    Cited by:

    1. Claudia Kirch, 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 270-275, June.
    2. Marie Hušková & Claudia Kirch, 2010. "A note on studentized confidence intervals for the change-point," Computational Statistics, Springer, vol. 25(2), pages 269-289, June.
    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;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 265-269, June.

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