Clustering Then Estimation of Spatio-Temporal Self-Exciting Processes

Haoting Zhang (), Donglin Zhan (), James Anderson (), Rhonda Righter () and Zeyu Zheng ()
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Haoting Zhang: Industrial Engineering and Operations Research Department, University of California Berkeley, Berkeley, California 94720
Donglin Zhan: Department of Electrical Engineering, Columbia University, New York, New York 10027
James Anderson: Department of Electrical Engineering, Columbia University, New York, New York 10027
Rhonda Righter: Industrial Engineering and Operations Research Department, University of California Berkeley, Berkeley, California 94720
Zeyu Zheng: Industrial Engineering and Operations Research Department, University of California Berkeley, Berkeley, California 94720

INFORMS Journal on Computing, 2025, vol. 37, issue 4, 874-893

Abstract: We propose a new estimation procedure for general spatio-temporal point processes that include a self-exciting feature. Estimating spatio-temporal self-exciting point processes with observed data is challenging, partly because of the difficulty in computing and optimizing the likelihood function. To circumvent this challenge, we employ a Poisson cluster representation for spatio-temporal self-exciting point processes to simplify the likelihood function and develop a new estimation procedure called “clustering-then-estimation” (CTE), which integrates clustering algorithms with likelihood-based estimation methods. Compared with the widely used expectation-maximization (EM) method, our approach separates the cluster structure inference of the data from the model selection. This has the benefit of reducing the risk of model misspecification. Our approach is computationally more efficient because it does not need to recursively solve optimization problems, which would be needed for EM. We also present asymptotic statistical results for our approach as theoretical support. Experimental results on several synthetic and real data sets illustrate the effectiveness of the proposed CTE procedure.

Keywords: spatio-temporal self-exciting point process; maximum likelihood estimation; clustering algorithm (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:37:y:2025:i:4:p:874-893

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