IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i1d10.1007_s11009-023-09991-4.html
   My bibliography  Save this article

Model Misspecification in Discrete Time Bayesian Online Change Detection

Author

Listed:
  • Savas Dayanik

    (Bilkent University)

  • Semih O Sezer

    (Sabancı University)

Abstract

We revisit the classical formulation of the discrete time Bayesian online change detection problem in which the common distribution of an observed sequence of random variables changes at an unknown point in time. The objective is to detect the change with a stopping time of the observations and minimize a given Bayes risk. When the change time has a zero-modified geometric prior distribution, the first crossing time of the odds-ratio process over a threshold is known to be an optimal solution. In the current paper, we consider a modeler who misspecifies some of the elements of this formulation. Because of this misspecification, the modeler computes a wrong stopping threshold and follows an incorrect odds-ratio process in implementation. To find her actual Bayes risk, which is different from the value function evaluated with the wrong choices, one needs to compute the expected costs accumulated by the true odds-ratio process until modeler’s odd-ratio process crosses this wrong boundary. In the paper, we carry out these computations in the extended state space of both processes, and we illustrate these computations on examples. In those examples, we construct tolerance regions for the parameters to be estimated by the modeler. For a given choice by the modeler, the tolerance region is the set of true values for which her relative loss is less than or equal to a predetermined level.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09991-4
    DOI: 10.1007/s11009-023-09991-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-09991-4
    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/s11009-023-09991-4?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. Blanchet-Scalliet, Christophette & Diop, Awa & Gibson, Rajna & Talay, Denis & Tanre, Etienne, 2007. "Technical analysis compared to mathematical models based methods under parameters mis-specification," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1351-1373, May.
    2. Aleksey S. Polunchenko & Alexander G. Tartakovsky, 2012. "State-of-the-Art in Sequential Change-Point Detection," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 649-684, September.
    3. Savas Dayanik & Christian Goulding & H. Vincent Poor, 2008. "Bayesian Sequential Change Diagnosis," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 475-496, May.
    4. 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.
    5. Savas Dayanik & Semih Onur Sezer, 2006. "Compound Poisson Disorder Problem," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 649-672, November.
    6. A. N. Shiryaev & M. V. Zhitlukhin & W. T. Ziemba, 2015. "Land and stock bubbles, crashes and exit strategies in Japan circa 1990 and in 2013," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1449-1469, September.
    7. 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.
    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. 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.
    4. Asaf Cohen & Eilon Solan, 2013. "Bandit Problems with Lévy Processes," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 92-107, February.
    5. 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).
    6. 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.
    7. Savas Dayanik & Semih Onur Sezer, 2006. "Compound Poisson Disorder Problem," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 649-672, November.
    8. 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.
    9. Bajgrowicz, Pierre & Scaillet, Olivier, 2012. "Technical trading revisited: False discoveries, persistence tests, and transaction costs," Journal of Financial Economics, Elsevier, vol. 106(3), pages 473-491.
    10. repec:hum:wpaper:sfb649dp2006-074 is not listed on IDEAS
    11. 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.
    12. 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.
    13. Robert A. Jarrow & Simon S. Kwok, 2021. "Inferring financial bubbles from option data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 1013-1046, November.
    14. Friesen, Geoffrey C. & Weller, Paul A. & Dunham, Lee M., 2009. "Price trends and patterns in technical analysis: A theoretical and empirical examination," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1089-1100, June.
    15. Hu, Yang & Oxley, Les, 2018. "Bubble contagion: Evidence from Japan’s asset price bubble of the 1980-90s," Journal of the Japanese and International Economies, Elsevier, vol. 50(C), pages 89-95.
    16. Lleo, Sebastien & Ziemba, William, 2017. "A tale of two indexes: predicting equity market downturns in China," LSE Research Online Documents on Economics 85131, London School of Economics and Political Science, LSE Library.
    17. Savas Dayanik & Warren Powell & Kazutoshi Yamazaki, 2013. "Asymptotically optimal Bayesian sequential change detection and identification rules," Annals of Operations Research, Springer, vol. 208(1), pages 337-370, September.
    18. Isakov, Dusan & Marti, Didier, 2011. "Technical Analysis with a Long-Term Perspective: Trading Strategies and Market Timing Ability," FSES Working Papers 421, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    19. Pavel V. Gapeev, 2016. "Bayesian Switching Multiple Disorder Problems," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1108-1124, August.
    20. Wu, Xu & Wang, Pei-Yu & Wang, Kun, 2023. "The effect of stabilization fund to rescue stock market based on expected return-capita circulation equation," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).
    21. Shiryaev Albert & Novikov Alexander A., 2009. "On a stochastic version of the trading rule “Buy and Hold”," Statistics & Risk Modeling, De Gruyter, vol. 26(4), pages 289-302, July.

    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:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09991-4. 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.