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On change-points tests based on two-samples U-Statistics for weakly dependent observations

Author

Listed:
  • Joseph Ngatchou-Wandji

    (EHESP Sorbonne Paris Cité & Institut Élie Cartan de Lorraine)

  • Echarif Elharfaoui

    (Université Chouaîb Doukkali)

  • Michel Harel

    (INSPÉ Limoges
    IMT, UMR 5219 UPS)

Abstract

We study change-points tests based on U-statistics for absolutely regular observations. Our method avoids some technical assumptions on the data and the kernel. The asymptotic properties of the U-statistics are studied under the null hypothesis, under fixed alternatives and under a sequence of local alternatives. The asymptotic distributions of the test statistics under the null hypothesis and under the local alternatives are given explicitly and the tests are shown to be consistent. A small set of simulations is done for evaluating the performance of the tests in detecting changes in the mean, variance and autocorrelation of some simple time series.

Suggested Citation

  • Joseph Ngatchou-Wandji & Echarif Elharfaoui & Michel Harel, 2022. "On change-points tests based on two-samples U-Statistics for weakly dependent observations," Statistical Papers, Springer, vol. 63(1), pages 287-316, February.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:1:d:10.1007_s00362-021-01242-3
    DOI: 10.1007/s00362-021-01242-3
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    1. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    2. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    3. Harel, Michel & Puri, Madan L., 1989. "Limiting behavior of U-statistics, V-statistics, and one sample rank order statistics for nonstationary absolutely regular processes," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 181-204, August.
    4. Alfredas Račkauskas & Martin Wendler, 2020. "Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment," Statistical Papers, Springer, vol. 61(4), pages 1409-1435, August.
    5. A. N. Pettitt, 1979. "A Non‐Parametric Approach to the Change‐Point Problem," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(2), pages 126-135, June.
    6. Bardet, Jean-Marc & Kengne, William, 2014. "Monitoring procedure for parameter change in causal time series," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 204-221.
    7. Ciuperca, Gabriela, 2011. "A general criterion to determine the number of change-points," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1267-1275, August.
    8. Gombay, Edit & Serban, Daniel, 2009. "Monitoring parameter change in time series models," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 715-725, April.
    9. Ashish Sen & S. Srivastava, 1975. "On tests for detecting change in mean when variance is unknown," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 479-486, December.
    10. Herold Dehling & Aeneas Rooch & Murad S. Taqqu, 2013. "Non-Parametric Change-Point Tests for Long-Range Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 153-173, March.
    11. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    12. Maria Mohr & Leonie Selk, 2020. "Estimating change points in nonparametric time series regression models," Statistical Papers, Springer, vol. 61(4), pages 1437-1463, August.
    13. Qing Yang & Yu-Ning Li & Yi Zhang, 2020. "Change point detection for nonparametric regression under strongly mixing process," Statistical Papers, Springer, vol. 61(4), pages 1465-1506, August.
    14. Lijing Ma & Andrew J. Grant & Georgy Sofronov, 2020. "Multiple change point detection and validation in autoregressive time series data," Statistical Papers, Springer, vol. 61(4), pages 1507-1528, August.
    15. Yujiao Yang & Qiongxia Song, 2014. "Jump detection in time series nonparametric regression models: a polynomial spline approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 325-344, April.
    16. Christian Francq & Jean‐Michel Zakoïan, 2012. "Strict Stationarity Testing and Estimation of Explosive and Stationary Generalized Autoregressive Conditional Heteroscedasticity Models," Econometrica, Econometric Society, vol. 80(2), pages 821-861, March.
    17. William Charky Kengne, 2012. "Testing for parameter constancy in general causal time‐series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 503-518, May.
    18. Huh, Jib, 2010. "Detection of a change point based on local-likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1681-1700, August.
    19. Chen, Kuo-mei & Cohen, Arthur & Sackrowitz, Harold, 2011. "Consistent multiple testing for change points," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1339-1343, November.
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    Keywords

    60F17; 62F03; 62M10;
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