IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i5p710-d1597291.html
   My bibliography  Save this article

A Self-Normalized Online Monitoring Method Based on the Characteristic Function

Author

Listed:
  • Yang Wang

    (Department of Statistics, School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China)

  • Baoying Yang

    (Department of Statistics, School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China)

Abstract

The goal of nonparametric online monitoring methods is to quickly detect structural changes in the distribution of a data stream. This work is concerned with a nonparametric self-normalized monitoring method based on the difference of empirical characteristic functions. This method introduces an additional self-normalization factor, which enables effective control the Type I error. We theoretically investigate the asymptotic properties of the monitoring method under the null hypothesis as well as the alternative hypothesis. Since the asymptotic distribution under the null hypothesis is quite complicated, we apply the multivariate stationary bootstrap method to estimate the critical value of the sequential test. Numerical simulations and a real-world application demonstrate the usefulness of the proposed method.

Suggested Citation

  • Yang Wang & Baoying Yang, 2025. "A Self-Normalized Online Monitoring Method Based on the Characteristic Function," Mathematics, MDPI, vol. 13(5), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:710-:d:1597291
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/5/710/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/5/710/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Raanju R. Sundararajan & Mohsen Pourahmadi, 2018. "Nonparametric change point detection in multivariate piecewise stationary time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(4), pages 926-956, October.
    2. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos G. Meintanis, 2017. "Fourier--type tests involving martingale difference processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 468-492, April.
    3. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    4. Andrew Patton & Dimitris Politis & Halbert White, 2009. "Correction to “Automatic Block-Length Selection for the Dependent Bootstrap” by D. Politis and H. White," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 372-375.
    5. Holger Dette & Josua Gösmann, 2020. "A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1361-1377, July.
    6. Horváth, Lajos & Kokoszka, Piotr & Zhang, Aonan, 2006. "Monitoring Constancy Of Variance In Conditionally Heteroskedastic Time Series," Econometric Theory, Cambridge University Press, vol. 22(3), pages 373-402, June.
    7. Alexander Aue & Claudia Kirch, 2024. "The state of cumulative sum sequential changepoint testing 70 years after Page," Biometrika, Biometrika Trust, vol. 111(2), pages 367-391.
    8. Okyoung Na & Youngmi Lee & Sangyeol Lee, 2011. "Monitoring parameter change in time series models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 171-199, June.
    9. Claudia Kirch & Christina Stoehr, 2022. "Sequential change point tests based on U‐statistics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1184-1214, September.
    10. Jentsch, Carsten & Subba Rao, Suhasini, 2015. "A test for second order stationarity of a multivariate time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 124-161.
    11. Lingzhe Guo & Reza Modarres, 2022. "Two multivariate online change detection models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(2), pages 427-448, January.
    12. Alexander Aue & Lajos Horváth & Piotr Kokoszka & Josef Steinebach, 2008. "Monitoring shifts in mean: Asymptotic normality of stopping times," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 515-530, November.
    13. Shao, Xiaofeng & Zhang, Xianyang, 2010. "Testing for Change Points in Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1228-1240.
    14. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-1065, September.
    15. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    Full references (including those not matched with items on IDEAS)

    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. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. 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.
    3. Hoga, Yannick, 2017. "Monitoring multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 105-121.
    4. Ariyarathne, Sakitha & Gangammanavar, Harsha & Sundararajan, Raanju R., 2022. "Change point detection-based simulation of nonstationary sub-hourly wind time series," Applied Energy, Elsevier, vol. 310(C).
    5. Castrillón-Candás, Julio E. & Kon, Mark, 2022. "Anomaly detection: A functional analysis perspective," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. William Kengne & Isidore S. Ngongo, 2022. "Inference for nonstationary time series of counts with application to change-point problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 801-835, August.
    7. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    8. Fabrizio Ghezzi & Eduardo Rossi & Lorenzo Trapani, 2024. "Fast Online Changepoint Detection," Papers 2402.04433, arXiv.org.
    9. KUROZUMI, Eiji & 黒住, 英司, 2016. "Monitoring Parameter Constancy with Endogenous Regressors," Discussion Papers 2016-01, Graduate School of Economics, Hitotsubashi University.
    10. Axel Bücher & Holger Dette & Florian Heinrichs, 2020. "Detecting deviations from second-order stationarity in locally stationary functional time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1055-1094, August.
    11. Simos G. Meintanis & Joseph Ngatchou-Wandji & James Allison, 2018. "Testing for serial independence in vector autoregressive models," Statistical Papers, Springer, vol. 59(4), pages 1379-1410, December.
    12. Jin, Lei & Cai, Li & Wang, Suojin, 2025. "Testing the constancy of the variance for time series with a trend," Computational Statistics & Data Analysis, Elsevier, vol. 208(C).
    13. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2017. "Tests for Structural Changes in Time Series of Counts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 843-865, December.
    14. 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.
    15. Josua Gösmann & Tobias Kley & Holger Dette, 2021. "A new approach for open‐end sequential change point monitoring," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(1), pages 63-84, January.
    16. Andreou, Elena & Ghysels, Eric, 2008. "Quality control for structural credit risk models," Journal of Econometrics, Elsevier, vol. 146(2), pages 364-375, October.
    17. Simos G. Meintanis & Joseph Ngatchou-Wandji & Šárka Hudecová, 2025. "Omnibus diagnostic procedures for vector multiplicative errors models," Statistical Papers, Springer, vol. 66(2), pages 1-44, February.
    18. Yu Jeffrey Hu & Jeroen Rombouts & Ines Wilms, 2025. "MLOps Monitoring at Scale for Digital Platforms," Papers 2504.16789, arXiv.org.
    19. Hsu, Chih-Chiang, 2007. "The MOSUM of squares test for monitoring variance changes," Finance Research Letters, Elsevier, vol. 4(4), pages 254-260, December.
    20. Mikkel Bennedsen, 2021. "Designing a statistical procedure for monitoring global carbon dioxide emissions," Climatic Change, Springer, vol. 166(3), pages 1-19, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:gam:jmathe:v:13:y:2025:i:5:p:710-:d:1597291. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.