Gradient-based estimation of linear Hawkes processes with general kernels

2021/11/20 by Álvaro Cartea, Cartea, Álvaro, Samuel N. Cohen +3
Mathematics · #60G55 #62M09 #90C52 #93E10 #FOS: Computer and information sciences #Methodology (stat.ME) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2111.10637

openalex publication_date 2021/11/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Linear multivariate Hawkes processes (MHP) are a fundamental class of point processes with self-excitation. When estimating parameters for these processes, a difficulty is that the two main error functionals, the log-likelihood and the least squares error (LSE), as well as the evaluation of their gradients, have a quadratic complexity in the number of observed events. In practice, this prohibits the use of exact gradient-based algorithms for parameter estimation. We construct an adaptive stratified sampling estimator of the gradient of the LSE. This results in a fast parametric estimation method for MHP with general kernels, applicable to large datasets, which compares favourably with existing methods.

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