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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
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