IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v8y2006i1d10.1007_s11009-006-7288-z.html
   My bibliography  Save this article

Approximate Simulation of Hawkes Processes

Author

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-006-7288-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-006-7288-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Angelos Dassios & Hongbiao Zhao, 2017. "Efficient Simulation of Clustering Jumps with CIR Intensity," Operations Research, INFORMS, vol. 65(6), pages 1494-1515, December.
    4. Jakob Gulddahl Rasmussen, 2013. "Bayesian Inference for Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 623-642, September.
    5. Martin Magris, 2019. "On the simulation of the Hawkes process via Lambert-W functions," Papers 1907.09162, arXiv.org.
    6. 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.
    7. 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.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dewei Wang & Chendi Jiang & Chanseok Park, 2019. "Reliability analysis of load-sharing systems with memory," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 341-360, April.
    2. Jamie Olson & Kathleen Carley, 2013. "Exact and approximate EM estimation of mutually exciting hawkes processes," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 63-80, April.
    3. van den Hengel, G. & Franses, Ph.H.B.F., 2018. "Forecasting social conflicts in Africa using an Epidemic Type Aftershock Sequence model," Econometric Institute Research Papers EI2018-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Chenlong Li & Zhanjie Song & Wenjun Wang, 2020. "Space–time inhomogeneous background intensity estimators for semi-parametric space–time self-exciting point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 945-967, August.
    5. Sebastian Meyer & Johannes Elias & Michael Höhle, 2012. "A Space–Time Conditional Intensity Model for Invasive Meningococcal Disease Occurrence," Biometrics, The International Biometric Society, vol. 68(2), pages 607-616, June.
    6. Lizhen Xu & Jason A. Duan & Andrew Whinston, 2014. "Path to Purchase: A Mutually Exciting Point Process Model for Online Advertising and Conversion," Management Science, INFORMS, vol. 60(6), pages 1392-1412, June.
    7. 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.
    8. Giada Adelfio & Arianna Agosto & Marcello Chiodi & Paolo Giudici, 2021. "Financial contagion through space-time point processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 665-688, June.
    9. Fama, Yuchen & Pozdnyakov, Vladimir, 2011. "A test for self-exciting clustering mechanism," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1541-1546, October.
    10. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Exploiting Spillovers to Forecast Crashes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(8), pages 936-955, December.
    11. Jiménez, Abigail, 2011. "Comparison of the Hurst and DEA exponents between the catalogue and its clusters: The California case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2146-2154.
    12. Sobin Joseph & Shashi Jain, 2024. "Non-Parametric Estimation of Multi-dimensional Marked Hawkes Processes," Papers 2402.04740, arXiv.org.
    13. Martin Magris, 2019. "On the simulation of the Hawkes process via Lambert-W functions," Papers 1907.09162, arXiv.org.
    14. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2012. "Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 883-894, September.
    15. Md. Asaduzzaman & A. Latif, 2014. "A parametric Markov renewal model for predicting tropical cyclones in Bangladesh," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 73(2), pages 597-612, September.
    16. Vipul Aggarwal & Elina H. Hwang & Yong Tan, 2021. "Learning to Be Creative: A Mutually Exciting Spatiotemporal Point Process Model for Idea Generation in Open Innovation," Information Systems Research, INFORMS, vol. 32(4), pages 1214-1235, December.
    17. Frederic Paik Schoenberg & Marc Hoffmann & Ryan J. Harrigan, 2019. "A recursive point process model for infectious diseases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1271-1287, October.
    18. Weijin Xu & Jian Wu & Mengtan Gao, 2023. "Temporal distribution model and occurrence probability of M ≥ 6.5 earthquakes in North China Seismic Zone," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 119(1), pages 125-141, October.
    19. Hainaut, Donatien, 2021. "Moment generating function of non-Markov self-excited claims processes," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 406-424.
    20. Ketelbuters, John John & Hainaut, Donatien, 2021. "Time-Consistent Evaluation of Credit Risk with Contagion," LIDAM Discussion Papers ISBA 2021004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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:spr:metcap:v:8:y:2006:i:1:d:10.1007_s11009-006-7288-z. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.