New Zealand Statistical Association 2024 Conference

Matt Pyper

University of Otago

Poster display: Statistical evaluation of neural network Hawkes processes

This is joint work with Conor Kresin

Hawkes processes are widely used to model point process data that exhibit self-excitation or inhibition, with applications spanning seismic activity, high-frequency stock trading, contagious disease spread, and neuronal activity. While Hawkes models provide interpretable parameters, they are often inflexible and computationally expensive to fit. Recently, continuous-time long short-term memory (LSTM) neural networks have been used to estimate the conditional intensity functions of Hawkes processes, enhancing their expressive power. This work presents a toolkit to assess the goodness of fit for neural Hawkes processes and explore the benefits of increased expressivity in a semi-parametric framework. Specifically, a KS-test based on the random time change theorem and residual analysis techniques commonly used for point processes are implemented. Additionally, cost function comparisons are described, including implementations of likelihood, least squares, and the Stoyan-Grabarnik estimator.