IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i4d10.1007_s00362-020-01196-y.html
   My bibliography  Save this article

Change point detection for nonparametric regression under strongly mixing process

Author

Listed:
  • Qing Yang

    (Zhejiang University)

  • Yu-Ning Li

    (Zhejiang University)

  • Yi Zhang

    (Zhejiang University)

Abstract

In this article, we consider the estimation of the structural change point in the nonparametric model with dependent observations. We introduce a maximum-CUSUM-estimation procedure, where the CUSUM statistic is constructed based on the sum-of-squares aggregation of the difference of the two Nadaraya-Watson estimates using the observations before and after a specific time point. Under some mild conditions, we prove that the statistic tends to zero almost surely if there is no change, and is larger than a threshold asymptotically almost surely otherwise, which helps us to obtain a threshold-detection strategy. Furthermore, we demonstrate the strong consistency of the change point estimator. In the simulation, we discuss the selection of the bandwidth and the threshold used in the estimation, and show the robustness of our method in the long-memory scenario. We implement our method to the data of Nasdaq 100 index and find that the relation between the realized volatility and the return exhibits several structural changes in 2007–2009.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-020-01196-y
    DOI: 10.1007/s00362-020-01196-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-020-01196-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-020-01196-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    2. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    3. Bandi, Federico M. & Renò, Roberto, 2012. "Time-varying leverage effects," Journal of Econometrics, Elsevier, vol. 169(1), pages 94-113.
    4. Haeran Cho & Piotr Fryzlewicz, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 475-507, March.
    5. Ting Zhang & Liliya Lavitas, 2018. "Unsupervised Self-Normalized Change-Point Testing for Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 637-648, April.
    6. Jin, Xiaoye, 2017. "Time-varying return-volatility relation in international stock markets," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 157-173.
    7. Fuqi Chen & Sévérien Nkurunziza, 2017. "On estimation of the change points in multivariate regression models with structural changes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 7157-7173, July.
    8. Maria Mohr & Leonie Selk, 2020. "Estimating change points in nonparametric time series regression models," Statistical Papers, Springer, vol. 61(4), pages 1437-1463, August.
    9. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(3), pages 315-352, June.
    10. Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    11. Jan Johannes & Suhasini Rao, 2011. "Nonparametric estimation for dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 661-681.
    12. Bollerslev, Tim & Zhou, Hao, 2006. "Volatility puzzles: a simple framework for gauging return-volatility regressions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 123-150.
    13. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    14. Hušková M. & Steinebach J., 2002. "Asymptotic Tests For Gradual Changes," Statistics & Risk Modeling, De Gruyter, vol. 20(1-4), pages 137-152, April.
    15. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    16. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    17. Alexander Aue & Gregory Rice & Ozan Sönmez, 2018. "Detecting and dating structural breaks in functional data without dimension reduction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 509-529, June.
    18. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
    19. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    20. Johannes, Jan & Subba Roa, Suhasini, 2011. "Nonparametric estimation for dependent data," LIDAM Reprints ISBA 2011048, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Baolong Ying & Qijing Yan & Zehua Chen & Jinchao Du, 2024. "A sequential feature selection approach to change point detection in mean-shift change point models," Statistical Papers, Springer, vol. 65(6), pages 3893-3915, August.
    2. 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.
    3. Georgy Sofronov & Martin Wendler & Volkmar Liebscher, 2020. "Editorial for the special issue: Change point detection," Statistical Papers, Springer, vol. 61(4), pages 1347-1349, August.
    4. Yang, Qing & Zhang, Yi, 2022. "Change-point detection for the link function in a single-index model," Statistics & Probability Letters, Elsevier, vol. 186(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    2. Jiang, Feiyu & Zhao, Zifeng & Shao, Xiaofeng, 2023. "Time series analysis of COVID-19 infection curve: A change-point perspective," Journal of Econometrics, Elsevier, vol. 232(1), pages 1-17.
    3. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    4. 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.
    5. Cui, Junfeng & Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2023. "Change-point testing for parallel data sets with FDR control," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    6. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Ma, Chenchen & Tu, Yundong, 2023. "Group fused Lasso for large factor models with multiple structural breaks," Journal of Econometrics, Elsevier, vol. 233(1), pages 132-154.
    8. Mengjia Yu & Xiaohui Chen, 2021. "Finite sample change point inference and identification for high‐dimensional mean vectors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 247-270, April.
    9. Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    10. Rice, Gregory & Zhang, Chi, 2022. "Consistency of binary segmentation for multiple change-point estimation with functional data," Statistics & Probability Letters, Elsevier, vol. 180(C).
    11. Oleksandr Gromenko & Piotr Kokoszka & Matthew Reimherr, 2017. "Detection of change in the spatiotemporal mean function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 29-50, January.
    12. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    13. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    14. Hong, Yongmiao & Linton, Oliver & McCabe, Brendan & Sun, Jiajing & Wang, Shouyang, 2024. "Kolmogorov–Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach," Journal of Econometrics, Elsevier, vol. 238(2).
    15. Chen, Likai & Wang, Weining & Wu, Wei Biao, 2019. "Inference of Break-Points in High-Dimensional Time Series," IRTG 1792 Discussion Papers 2019-013, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. V. Brault & C. Lévy-Leduc & A. Mathieu & A. Jullien, 2018. "Change-Point Estimation in the Multivariate Model Taking into Account the Dependence: Application to the Vegetative Development of Oilseed Rape," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(3), pages 374-389, September.
    17. Cho, Haeran & Korkas, Karolos K., 2022. "High-dimensional GARCH process segmentation with an application to Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 23(C), pages 187-203.
    18. Pang, Tianxiao & Du, Lingjie & Chong, Terence Tai-Leung, 2021. "Estimating multiple breaks in nonstationary autoregressive models," Journal of Econometrics, Elsevier, vol. 221(1), pages 277-311.
    19. Shu, Lei & Chen, Yu & Zhang, Weiping & Wang, Xueqin, 2022. "Spatial rank-based high-dimensional change point detection via random integration," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    20. Hajra Siddiqa & Sajid Ali & Ismail Shah, 2021. "Most recent changepoint detection in censored panel data," Computational Statistics, Springer, vol. 36(1), pages 515-540, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-020-01196-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.