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Approximate Simulation of Hawkes Processes

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Listed:
  • Jesper Møller

    (Aalborg University)

  • Jakob G. Rasmussen

    (Aalborg University)

Abstract

Hawkes processes are important in point process theory and its applications, and simulation of such processes are often needed for various statistical purposes. This article concerns a simulation algorithm for unmarked and marked Hawkes processes, exploiting that the process can be constructed as a Poisson cluster process. The algorithm suffers from edge effects but is much faster than the perfect simulation algorithm introduced in our previous work Møller and Rasmussen (2004). We derive various useful measures for the error committed when using the algorithm, and we discuss various empirical results for the algorithm compared with perfect simulations. Extensions of the algorithm and the results to more general types of marked point processes are also discussed.

Suggested Citation

  • Jesper Møller & Jakob G. Rasmussen, 2006. "Approximate Simulation of Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 53-64, March.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:1:d:10.1007_s11009-006-7288-z
    DOI: 10.1007/s11009-006-7288-z
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    References listed on IDEAS

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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
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    Cited by:

    1. Jakob Gulddahl Rasmussen, 2013. "Bayesian Inference for Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 623-642, September.
    2. Martin Magris, 2019. "On the simulation of the Hawkes process via Lambert-W functions," Papers 1907.09162, arXiv.org.
    3. Dassios, Angelos & Zhao, Hongbiao, 2017. "Efficient simulation of clustering jumps with CIR intensity," LSE Research Online Documents on Economics 74205, London School of Economics and Political Science, LSE Library.
    4. V. Filimonov & D. Sornette, 2015. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1293-1314, August.
    5. Tomasz R. Bielecki & Jacek Jakubowski & Mariusz Niewęgłowski, 2022. "Construction and Simulation of Generalized Multivariate Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2865-2896, December.
    6. Møller, Jesper & Torrisi, Giovanni Luca, 2007. "The pair correlation function of spatial Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 995-1003, June.
    7. Angelos Dassios & Hongbiao Zhao, 2017. "Efficient Simulation of Clustering Jumps with CIR Intensity," Operations Research, INFORMS, vol. 65(6), pages 1494-1515, December.
    8. Jakob G. Rasmussen & Heidi S. Christensen, 2021. "Point Processes on Directed Linear Networks," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 647-667, June.

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