Gradient-based estimation of linear Hawkes processes with general kernels

Álvaro Cartea; Samuel N. Cohen; Saad Labyad

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arXiv · 2111.10637

Gradient-based estimation of linear Hawkes processes with general kernels

Álvaro Cartea·Samuel N. Cohen·Saad Labyad

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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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Álvaro Cartea, Samuel N. Cohen, Saad Labyad. 2021-11-20. Gradient-based estimation of linear Hawkes processes with general kernels. https://arxiv.org/abs/2111.10637

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