IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i2p325-344.html
   My bibliography  Save this article

Jump detection in time series nonparametric regression models: a polynomial spline approach

Author

Listed:
  • Yujiao Yang
  • Qiongxia Song

Abstract

For time series nonparametric regression models with discontinuities, we propose to use polynomial splines to estimate locations and sizes of jumps in the mean function. Under reasonable conditions, test statistics for the existence of jumps are given and their limiting distributions are derived under the null hypothesis that the mean function is smooth. Simulations are provided to check the powers of the tests. A climate data application and an application to the US unemployment rates of men and women are used to illustrate the performance of the proposed method in practice. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:2:p:325-344
    DOI: 10.1007/s10463-013-0411-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0411-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0411-3?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. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    2. Li Wang & Lijian Yang, 2010. "Simultaneous confidence bands for time-series prediction function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 999-1018.
    3. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2008. "Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility," Journal of Econometrics, Elsevier, vol. 143(2), pages 227-262, April.
    4. Shujie Ma & Lijian Yang, 2011. "A jump-detecting procedure based on spline estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 67-81.
    5. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    6. Wong, Heung & Ip, Waicheung & Li, Yuan, 2001. "Detection of jumps by wavelets in a heteroscedastic autoregressive model," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 365-372, May.
    7. Hui, Eddie C.M. & Yu, Carisa K.W. & Ip, Wai-Cheung, 2010. "Jump point detection for real estate investment success," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1055-1064.
    8. Zhou, Yong & Wan, Alan T.K. & Xie, Shangyu & Wang, Xiaojing, 2010. "Wavelet analysis of change-points in a non-parametric regression with heteroscedastic variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 183-201, November.
    9. Lin, Zhengyan & Li, Degui & Chen, Jia, 2008. "Change point estimators by local polynomial fits under a dependence assumption," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2339-2355, November.
    10. Müller, Hans-Georg & Song, Kai-Sheng, 1997. "Two-stage change-point estimators in smooth regression models," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 323-335, June.
    11. Jianhua Z. Huang & Lijian Yang, 2004. "Identification of non‐linear additive autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 463-477, May.
    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. 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.
    2. Han, Zhong-Cheng & Lin, Jin-Guan & Zhao, Yan-Yong, 2020. "Adaptive semiparametric estimation for single index models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 151(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. Jingle Wang & Ming Zheng, 2012. "Wavelet detection of change points in hazard rate models with censored dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 765-781.
    2. Shujie Ma & Yanyuan Ma & Yanqing Wang & Eli S. Kravitz & Raymond J. Carroll, 2017. "A Semiparametric Single-Index Risk Score Across Populations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1648-1662, October.
    3. L. Tang & Q. Shao, 2014. "Efficient Estimation For Periodic Autoregressive Coefficients Via Residuals," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 378-389, July.
    4. Zhou, Yong & Wan, Alan T.K. & Xie, Shangyu & Wang, Xiaojing, 2010. "Wavelet analysis of change-points in a non-parametric regression with heteroscedastic variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 183-201, November.
    5. Kohler, Michael & Krzyżak, Adam, 2015. "Estimation of a jump point in random design regression," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 247-255.
    6. Chen, Heng & Fan, Yanqin, 2019. "Identification and wavelet estimation of weighted ATE under discontinuous and kink incentive assignment mechanisms," Journal of Econometrics, Elsevier, vol. 212(2), pages 476-502.
    7. Cui, Yan & Yang, Jun & Zhou, Zhou, 2023. "State-domain change point detection for nonlinear time series regression," Journal of Econometrics, Elsevier, vol. 234(1), pages 3-27.
    8. Kang, Yicheng & Shi, Yueyong & Jiao, Yuling & Li, Wendong & Xiang, Dongdong, 2021. "Fitting jump additive models," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    9. Yujiao Yang & Yuhang Xu & Qiongxia Song, 2012. "Spline confidence bands for variance functions in nonparametric time series regressive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 699-714.
    10. Li Cai & Lisha Li & Simin Huang & Liang Ma & Lijian Yang, 2020. "Oracally efficient estimation for dense functional data with holiday effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 282-306, March.
    11. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    12. Casini, Alessandro & Perron, Pierre, 2024. "Change-point analysis of time series with evolutionary spectra," Journal of Econometrics, Elsevier, vol. 242(2).
    13. Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2020. "Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown Function," IRTG 1792 Discussion Papers 2020-008, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    14. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    15. Youngseon Lee & Seongil Jo & Jaeyong Lee, 2022. "A variational inference for the Lévy adaptive regression with multiple kernels," Computational Statistics, Springer, vol. 37(5), pages 2493-2515, November.
    16. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(4), pages 861-916, August.
    17. Shohei Tateishi & Sadanori Konishi, 2011. "Nonlinear regression modeling and detecting change points via the relevance vector machine," Computational Statistics, Springer, vol. 26(3), pages 477-490, September.
    18. Shiyi Chen & Wolfgang K. Härdle & Kiho Jeong, 2010. "Forecasting volatility with support vector machine-based GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(4), pages 406-433.
    19. Isabel Casas & Irene Gijbels, 2009. "Unstable volatility functions: the break preserving local linear estimator," CREATES Research Papers 2009-48, Department of Economics and Business Economics, Aarhus University.
    20. Hui, Eddie Chi-Man & Wang, Ziyou, 2015. "Can we predict the property cycle? A study of securitized property market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 72-87.

    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:aistmt:v:66:y:2014:i:2:p:325-344. 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.