IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2501.03434.html
   My bibliography  Save this paper

How to verify that a given process is a L\'evy-Driven Ornstein-Uhlenbeck Process

Author

Listed:
  • Ibrahim Abdelrazeq

    (Rhodes College)

  • Hardy Smith

    (Rhodes College)

  • Dinmukhammed Zhanbyrshy

    (Rhodes College)

Abstract

Assuming that a L\'evy-Driven Ornstein-Uhlenbeck (or CAR(1)) processes is observed at discrete times $0$, $h$, $2h$,$\cdots$ $[T/h]h$. We introduce a step-by-step methodological approach on how a person would verify the model assumptions. The methodology involves estimating the model parameters and approximating the driving process. We demonstrate how to use the increments of the approximated driving process, along with the estimated parameters, to test the assumptions that the CAR(1) process is L\'evy-driven. We then show how to test the hypothesis that the CAR(1) process belongs to a specified class of L\'evy processes. The performance of the tests is illustrated through multiple simulations. Finally, we demonstrate how to apply the methodology step-by-step to a variety of economic and financial data examples.

Suggested Citation

  • Ibrahim Abdelrazeq & Hardy Smith & Dinmukhammed Zhanbyrshy, 2025. "How to verify that a given process is a L\'evy-Driven Ornstein-Uhlenbeck Process," Papers 2501.03434, arXiv.org, revised Jan 2025.
    • Handle: RePEc:arx:papers:2501.03434
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2501.03434
    File Function: Latest version
    Download Restriction: no
    ---><---

    More about this item

    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:arx:papers:2501.03434. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.