{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/how-to-verify-that-a-given-process-is-a-levy","title":"How to verify that a given process is a Lévy-Driven Ornstein-Uhlenbeck Process","arxiv_id":"2501.03434","date":"2025-01-06","proceeding":null,"authors":["Ibrahim Abdelrazeq","Hardy Smith","Dinmukhammed Zhanbyrshy"],"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.","url_abs":"https://arxiv.org/abs/2501.03434v2","url_pdf":"https://arxiv.org/pdf/2501.03434v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"how-to-verify-that-a-given-process-is-a-levy","repo_url":"https://github.com/rhardysmith02/How-to-verify-that-a-given-process-is-a-L-evy-Driven-Ornstein-Uhlenbeck-Process","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}