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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.

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
    DOI: 10.1111/j.1467-9892.2008.00589.x
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    References listed on IDEAS

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    1. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    2. 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. 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.
    2. Maricela Cruz & Hernando Ombao & Daniel L. Gillen, 2022. "A Generalized Interrupted Time Series Model for Assessing Complex Health Care Interventions," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 582-610, December.
    3. Maria Mohr & Leonie Selk, 2020. "Estimating change points in nonparametric time series regression models," Statistical Papers, Springer, vol. 61(4), pages 1437-1463, August.
    4. 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.
    5. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    6. Shi, Xuesheng & Gallagher, Colin & Lund, Robert & Killick, Rebecca, 2022. "A comparison of single and multiple changepoint techniques for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    7. B. Cooper Boniece & Lajos Horváth & Peter M. Jacobs, 2024. "Change point detection in high dimensional data with U-statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 400-452, June.
    8. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
    9. W. Holmes Finch, 2019. "A Monte Carlo Simulation Study Assessing the Performance of a Bayesian Approach for Identifying Differences in Change Point Location for Two Time Series," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(3), pages 1-4.
    10. Cho, Haeran & Kirch, Claudia, 2022. "Bootstrap confidence intervals for multiple change points based on moving sum procedures," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    11. 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.

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