Maximum Likelihood Estimation for Hawkes Processes with self-excitation or inhibition

TL;DR

This paper introduces a maximum likelihood estimation method for univariate Hawkes processes that can handle both self-excitation and inhibition, improving accuracy especially in inhibition scenarios.

Contribution

It generalizes existing methods to include inhibition in Hawkes processes and demonstrates superior estimation accuracy with exponential kernels.

Findings

More accurate parameter estimation in inhibition cases

Generalization of estimation techniques to self-inhibition and excitation

Effective implementation with exponential kernels

Abstract

In this paper, we present a maximum likelihood method for estimating the parameters of a univariate Hawkes process with self-excitation or inhibition. Our work generalizes techniques and results that were restricted to the self-exciting scenario. The proposed estimator is implemented for the classical exponential kernel and we show that, in the inhibition context, our procedure provides more accurate estimations than current alternative approaches.