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Multivariate Hawkes processes with spatial covariates for spatiotemporal event data analysis

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Matthias Kirchner, 2017. "An estimation procedure for the Hawkes process," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 571-595, April.
    5. 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.
    6. 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.
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