IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v30y2025i1d10.1007_s13253-024-00653-7.html
   My bibliography  Save this article

Spatio-Temporal Hawkes Point Processes: A Review

Author

Listed:
  • Alba Bernabeu

    (University Jaume I)

  • Jiancang Zhuang

    (Research Organisation of Information and Systems
    The Graduate University for Advanced Studies
    London Mathematical Laboratory)

  • Jorge Mateu

    (University Jaume I)

Abstract

Hawkes processes are a particularly interesting class of stochastic point processes that were introduced in the early seventies by Alan Hawkes, notably to model the occurrence of seismic events. They are also called self-exciting point processes, in which the occurrence of an event increases the probability of occurrence of another event. The Hawkes process is characterized by a stochastic intensity, which represents the conditional probability density of the occurrence of an event in the immediate future, given the observations in the past. In this paper, we present some background and all major aspects of Hawkes processes, with a particular focus on simulation methods, and estimation techniques widely used in practical modeling aspects. We aim to provide a rich and self-contained overview of these stochastic processes as a way to have an overall vision of Hawkes processes in only one piece of paper. We also discuss possibilities for future research in the area of self-exciting processes.

Suggested Citation

  • Alba Bernabeu & Jiancang Zhuang & Jorge Mateu, 2025. "Spatio-Temporal Hawkes Point Processes: A Review," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(1), pages 89-119, March.
    • Handle: RePEc:spr:jagbes:v:30:y:2025:i:1:d:10.1007_s13253-024-00653-7
    DOI: 10.1007/s13253-024-00653-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-024-00653-7
    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/s13253-024-00653-7?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.
    2. Emmanuel Bacry & Jean-Fran�ois Muzy, 2014. "Hawkes model for price and trades high-frequency dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1147-1166, July.
    3. Kristensen, Kasper & Nielsen, Anders & Berg, Casper W. & Skaug, Hans & Bell, Bradley M., 2016. "TMB: Automatic Differentiation and Laplace Approximation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i05).
    4. Roger D. Peng & Frederic Paik Schoenberg & James A. Woods, 2005. "A Space-Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 26-35, March.
    5. Francesco Serafini & Finn Lindgren & Mark Naylor, 2023. "Approximation of Bayesian Hawkes process with inlabru," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    6. Schatz, Michael & Wheatley, Spencer & Sornette, Didier, 2022. "The ARMA Point Process and its Estimation," Econometrics and Statistics, Elsevier, vol. 24(C), pages 164-182.
    7. Mohler, G. O. & Short, M. B. & Brantingham, P. J. & Schoenberg, F. P. & Tita, G. E., 2011. "Self-Exciting Point Process Modeling of Crime," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 100-108.
    8. Jiancang Zhuang, 2006. "Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 635-653, September.
    9. Jiancang Zhuang & Jorge Mateu, 2019. "A semiparametric spatiotemporal Hawkes‐type point process model with periodic background for crime data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(3), pages 919-942, June.
    10. Diggle, Peter J. & Guan, Yongtao & Hart, Anthony C. & Paize, Fauzia & Stanton, Michelle, 2010. "Estimating Individual-Level Risk in Spatial Epidemiology Using Spatially Aggregated Information on the Population at Risk," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1394-1402.
    11. Peter J. Diggle & Irene Kaimi & Rosa Abellana, 2010. "Partial-Likelihood Analysis of Spatio-Temporal Point-Process Data," Biometrics, The International Biometric Society, vol. 66(2), pages 347-354, June.
    12. Biao Cai & Jingfei Zhang & Yongtao Guan, 2024. "Latent Network Structure Learning From High-Dimensional Multivariate Point Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 95-108, January.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Pierfrancesco Alaimo Di Loro & Marco Mingione & Paolo Fantozzi, 2025. "Semi-parametric Spatio-Temporal Hawkes Process for Modelling Road Accidents in Rome," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(1), pages 8-38, March.
    3. Kieran Kalair & Colm Connaughton & Pierfrancesco Alaimo Di Loro, 2021. "A non‐parametric Hawkes process model of primary and secondary accidents on a UK smart motorway," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 80-97, January.
    4. Jonas R. Brehmer & Tilmann Gneiting & Marcus Herrmann & Warner Marzocchi & Martin Schlather & Kirstin Strokorb, 2024. "Comparative evaluation of point process forecasts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 47-71, February.
    5. 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.
    6. 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.
    7. 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.
    8. Chenlong Li & Kaiyan Cui, 2024. "Multivariate Hawkes processes with spatial covariates for spatiotemporal event data analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(4), pages 535-578, August.
    9. 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.
    10. Emmanuel Bacry & Thibault Jaisson & Jean-Francois Muzy, 2014. "Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling," Papers 1412.7096, arXiv.org.
    11. 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.
    12. Jing Chen, 2025. "Editorial A Tribute to Professor Geoffrey Alan Hawkes (19 September 1938–9 November 2023)," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(1), pages 1-7, March.
    13. Roba Bairakdar & Debbie Dupuis & Melina Mailhot, 2024. "Deviance Voronoi Residuals for Space-Time Point Process Models: An Application to Earthquake Insurance Risk," Papers 2410.04369, arXiv.org.
    14. Naveed Chehrazi & Thomas A. Weber, 2015. "Dynamic Valuation of Delinquent Credit-Card Accounts," Management Science, INFORMS, vol. 61(12), pages 3077-3096, December.
    15. Giada Adelfio & Marcello Chiodi, 2021. "Including covariates in a space-time point process with application to seismicity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 947-971, September.
    16. Gresnigt, Francine & Kole, Erik & Franses, Philip Hans, 2015. "Interpreting financial market crashes as earthquakes: A new Early Warning System for medium term crashes," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 123-139.
    17. Zhang, Tonglin & Zhuang, Run, 2017. "Testing proportionality between the first-order intensity functions of spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 72-82.
    18. Jakob Gulddahl Rasmussen, 2013. "Bayesian Inference for Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 623-642, September.
    19. Conor Kresin & Frederic Schoenberg, 2023. "Parametric estimation of spatial–temporal point processes using the Stoyan–Grabarnik statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(6), pages 887-909, December.
    20. Stindl, Tom & Chen, Feng, 2018. "Likelihood based inference for the multivariate renewal Hawkes process," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 131-145.

    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:jagbes:v:30:y:2025:i:1:d:10.1007_s13253-024-00653-7. 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.