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High-Frequency Estimation of ITÔ Semimartingale Baseline for Hawkes Processes

Author

Listed:
  • Yoann Potiron

    (Keio University - Faculty of Business and Commerce)

  • O. Scaillet

    (Swiss Finance Institute - University of Geneva)

  • Vladimir Volkov

    (Tasmania School of Business and Economics, University of Tasmania)

  • Seunghyeon Yu

    (Northwestern University - Kellogg School of Management)

Abstract

We consider Hawkes self-exciting processes with a baseline driven by an Itô semimartingale with possible jumps. Under in-fill asymptotics, we characterize feasible statistics induced by central limit theory for empirical average and variance of local Poisson estimates. As a byproduct, we develop a test for the absence of a Hawkes component and a test for baseline constancy. Simulation studies corroborate the asymptotic theory. An empirical application on high-frequency data of the E-mini S&P500 future contracts shows that the absence of a Hawkes component and baseline constancy is always rejected.

Suggested Citation

  • Yoann Potiron & O. Scaillet & Vladimir Volkov & Seunghyeon Yu, 2025. "High-Frequency Estimation of ITÔ Semimartingale Baseline for Hawkes Processes," Swiss Finance Institute Research Paper Series 25-13, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2513
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    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5108542
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