IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v189y2025ics0304414925001425.html

Sequential common change detection, isolation, and estimation in multiple compound Poisson processes

Author

Listed:
  • Kim, Dong-Yun
  • Wu, Wei Biao
  • Wu, Yanhong

Abstract

We explore and compare the detection of changes in both the arrival rate and jump size mean and estimation of change-time after detection within a compound Poisson process by using generalized CUSUM and Shiryayev–Roberts (S–R) procedures. Average in-control and out-of control lengths are derived as well as the limiting distribution of the generalized CUSUM processes. The asymptotic bias of change time estimation is also derived. To detect a common change in multiple compound Poisson processes where change only occurs in a portion of panels, a unified algorithm is proposed that employs the sum of S–R processes to detect a common change, uses individual CUSUM processes to isolate the changed panels with False Discovery Rate (FDR) control, and then estimate the common change time as the median of the estimates obtained from the isolated channels. To illustrate the approach, we apply it to mining disaster data in the USA.

Suggested Citation

  • Kim, Dong-Yun & Wu, Wei Biao & Wu, Yanhong, 2025. "Sequential common change detection, isolation, and estimation in multiple compound Poisson processes," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:spapps:v:189:y:2025:i:c:s0304414925001425
    DOI: 10.1016/j.spa.2025.104701
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925001425
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104701?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Bayraktar, Erhan & Dayanik, Savas & Karatzas, Ioannis, 2005. "The standard Poisson disorder problem revisited," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1437-1450, September.
    2. Savas Dayanik & Semih Onur Sezer, 2006. "Compound Poisson Disorder Problem," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 649-672, November.
    3. Tina Herberts & Uwe Jensen, 2004. "Optimal Detection of a Change Point in a Poisson Process for Different Observation Schemes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 347-366, September.
    4. Gapeev, Pavel V., 2005. "The disorder problem for compound Poisson processes with exponential jumps," LSE Research Online Documents on Economics 3219, London School of Economics and Political Science, LSE Library.
    5. Yanhong Wu, 2019. "A combined SR-CUSUM procedure for detecting common changes in panel data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(17), pages 4302-4319, September.
    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. Krawiec, Michał & Palmowski, Zbigniew & Płociniczak, Łukasz, 2018. "Quickest drift change detection in Lévy-type force of mortality model," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 432-450.
    2. Erhan Bayraktar & H. Poor, 2008. "Optimal time to change premiums," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 125-158, August.
    3. Savas Dayanik & Semih O Sezer, 2023. "Model Misspecification in Discrete Time Bayesian Online Change Detection," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-27, March.
    4. Bruno Buonaguidi, 2023. "Finite Horizon Sequential Detection with Exponential Penalty for the Delay," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 224-238, July.
    5. Asaf Cohen & Eilon Solan, 2013. "Bandit Problems with Lévy Processes," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 92-107, February.
    6. Gapeev, Pavel V. & Stoev, Yavor I., 2017. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 152-162.
    7. Buonaguidi, B., 2022. "The disorder problem for diffusion processes with the ϵ-linear and expected total miss criteria," Statistics & Probability Letters, Elsevier, vol. 189(C).
    8. Pavel V. Gapeev & Yavor I. Stoev, 2025. "Quickest Change-point Detection Problems for Multidimensional Wiener Processes," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-25, March.
    9. Gapeev, Pavel V. & Jeanblanc, Monique, 2024. "On the construction of conditional probability densities in the Brownian and compound Poisson filtrations," LSE Research Online Documents on Economics 121059, London School of Economics and Political Science, LSE Library.
    10. Savas Dayanik & Semih Onur Sezer, 2006. "Compound Poisson Disorder Problem," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 649-672, November.
    11. repec:hum:wpaper:sfb649dp2006-074 is not listed on IDEAS
    12. Brown, Marlo, 2008. "Monitoring a Poisson process in several categories subject to changes in the arrival rates," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2637-2643, November.
    13. Ekström, Erik & Milazzo, Alessandro, 2024. "A detection problem with a monotone observation rate," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    14. Erhan Bayraktar & Savas Dayanik, 2006. "Poisson Disorder Problem with Exponential Penalty for Delay," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 217-233, May.
    15. Gapeev, Pavel V., 2020. "On the problems of sequential statistical inference for Wiener processes with delayed observations," LSE Research Online Documents on Economics 104072, London School of Economics and Political Science, LSE Library.
    16. S. Cawston & L. Vostrikova, 2010. "$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point," Papers 1004.3525, arXiv.org, revised Jun 2011.
    17. Brown, Marlo & Zacks, Shelemyahu, 2006. "A note on optimal stopping for possible change in the intensity of an ordinary Poisson process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1417-1425, July.
    18. Pavel V. Gapeev, 2016. "Bayesian Switching Multiple Disorder Problems," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1108-1124, August.
    19. repec:hum:wpaper:sfb649dp2006-068 is not listed on IDEAS
    20. Gapeev, Pavel V., 2006. "Multiple disorder problems for Wiener and compound Poisson processes with exponential jumps," SFB 649 Discussion Papers 2006-074, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    21. Pavel V. Gapeev & Oliver Brockhaus & Mathieu Dubois, 2018. "On Some Functionals Of The First Passage Times In Models With Switching Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-21, February.
    22. Savas Dayanik, 2010. "Wiener Disorder Problem with Observations at Fixed Discrete Time Epochs," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 756-785, November.

    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:eee:spapps:v:189:y:2025:i:c:s0304414925001425. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.