IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v76y2024i4d10.1007_s10463-023-00894-2.html
   My bibliography  Save this article

Multivariate Hawkes processes with spatial covariates for spatiotemporal event data analysis

Author

Listed:
  • Chenlong Li

    (Taiyuan University of Technology)

  • Kaiyan Cui

    (Shanxi University)

Abstract

Spatiotemporal events occur in many disciplines, including economics, sociology, criminology, and seismology, with different patterns in space and time related to environmental characteristics, policing, and human behavior. In this paper, we propose a class of multivariate Hawkes processes with spatial covariates to consider the influence structure of spatial features in spatiotemporal events and the spatiotemporal patterns such as clustering. Baseline intensities are assumed to be a spatial Poisson regression model to explain spatial feature influence. The transfer functions are considered unknown but smooth and decreasing to explain the clustering phenomena. A semiparametric estimation method based on time discretization and local constant approximation is introduced. Transfer function estimators are shown to be consistent, and baseline intensity estimators are consistent and asymptotically normal. We examine the numerical performance of the proposed estimators with extensive simulation and illustrate the application of the proposed model to crime data obtained from Pittsburgh, Pennsylvania.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:4:d:10.1007_s10463-023-00894-2
    DOI: 10.1007/s10463-023-00894-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-023-00894-2
    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/s10463-023-00894-2?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. Matthias Kirchner, 2017. "An estimation procedure for the Hawkes process," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 571-595, April.
    2. Schoenberg F.P., 2003. "Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 789-795, January.
    3. 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.
    4. Baichuan Yuan & Frederic P. Schoenberg & Andrea L. Bertozzi, 2021. "Fast estimation of multivariate spatiotemporal Hawkes processes and network reconstruction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1127-1152, December.
    5. 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.
    6. Junhyung Park & Frederic Paik Schoenberg & Andrea L. Bertozzi & P. Jeffrey Brantingham, 2021. "Investigating Clustering and Violence Interruption in Gang-Related Violent Crime Data Using Spatial–Temporal Point Processes With Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1674-1687, October.
    7. Veen, Alejandro & Schoenberg, Frederic P., 2008. "Estimation of SpaceTime Branching Process Models in Seismology Using an EMType Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 614-624, June.
    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. 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.
    2. Brantingham, P. Jeffrey & Carter, Jeremy & MacDonald, John & Melde, Chris & Mohler, George, 2021. "Is the recent surge in violence in American cities due to contagion?," Journal of Criminal Justice, Elsevier, vol. 76(C).
    3. Mohler, George, 2014. "Marked point process hotspot maps for homicide and gun crime prediction in Chicago," International Journal of Forecasting, Elsevier, vol. 30(3), pages 491-497.
    4. Angelos Dassios & Hongbiao Zhao, 2017. "A Generalized Contagion Process With An Application To Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-33, February.
    5. 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.
    6. Jakob Gulddahl Rasmussen, 2013. "Bayesian Inference for Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 623-642, September.
    7. 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.
    8. Mohler, George & Carter, Jeremy & Raje, Rajeev, 2018. "Improving social harm indices with a modulated Hawkes process," International Journal of Forecasting, Elsevier, vol. 34(3), pages 431-439.
    9. Alex Reinhart & Joel Greenhouse, 2018. "Self‐exciting point processes with spatial covariates: modelling the dynamics of crime," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1305-1329, November.
    10. Eric W. Fox & Martin B. Short & Frederic P. Schoenberg & Kathryn D. Coronges & Andrea L. Bertozzi, 2016. "Modeling E-mail Networks and Inferring Leadership Using Self-Exciting Point Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 564-584, April.
    11. Dassios, Angelos & Zhao, Hongbiao, 2017. "A generalised contagion process with an application to credit risk," LSE Research Online Documents on Economics 68558, London School of Economics and Political Science, LSE Library.
    12. Chen, Zezhun & Dassios, Angelos, 2022. "Cluster point processes and Poisson thinning INARMA," LSE Research Online Documents on Economics 113652, London School of Economics and Political Science, LSE Library.
    13. Baichuan Yuan & Frederic P. Schoenberg & Andrea L. Bertozzi, 2021. "Fast estimation of multivariate spatiotemporal Hawkes processes and network reconstruction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1127-1152, December.
    14. Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    15. 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.
    16. Cavaliere, Giuseppe & Lu, Ye & Rahbek, Anders & Stærk-Østergaard, Jacob, 2023. "Bootstrap inference for Hawkes and general point processes," Journal of Econometrics, Elsevier, vol. 235(1), pages 133-165.
    17. Boswijk, H. Peter & Laeven, Roger J.A. & Yang, Xiye, 2018. "Testing for self-excitation in jumps," Journal of Econometrics, Elsevier, vol. 203(2), pages 256-266.
    18. repec:jss:jstsof:08:i16 is not listed on IDEAS
    19. 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.
    20. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    21. Thibault Jaisson & Mathieu Rosenbaum, 2015. "Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes," Papers 1504.03100, arXiv.org.

    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:aistmt:v:76:y:2024:i:4:d:10.1007_s10463-023-00894-2. 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.