IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v210y2025ics0167947325000726.html
   My bibliography  Save this article

A goodness-of-fit test for geometric Brownian motion

Author

Listed:
  • Gaigall, Daniel
  • Wübbolding, Philipp

Abstract

A new goodness-of-fit test for the composite null hypothesis that data originate from a geometric Brownian motion is studied in the functional data setting. This is equivalent to testing if the data are from a scaled Brownian motion with linear drift. Critical values for the test are obtained, ensuring that the specified significance level is achieved in finite samples. The asymptotic behavior of the test statistic under the null distribution and alternatives is studied, and it is also demonstrated that the test is consistent. Furthermore, the proposed approach offers advantages in terms of fast and simple implementation. A comprehensive simulation study shows that the power of the new test compares favorably to that of existing methods. A key application is the assessment of financial time series for the suitability of the Black-Scholes model. Examples relating to various stock and interest rate time series are presented in order to illustrate the proposed test.

Suggested Citation

  • Gaigall, Daniel & Wübbolding, Philipp, 2025. "A goodness-of-fit test for geometric Brownian motion," Computational Statistics & Data Analysis, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:csdana:v:210:y:2025:i:c:s0167947325000726
    DOI: 10.1016/j.csda.2025.108196
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947325000726
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2025.108196?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.

    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:csdana:v:210:y:2025:i:c:s0167947325000726. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/locate/csda .

    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.