Maximum Likelihood Estimation for Hawkes Processes with self-excitation or inhibition
This work addresses a methodological gap for researchers modeling point processes with inhibition, though it is incremental as it extends known techniques to a broader scenario.
The authors tackled the problem of parameter estimation for univariate Hawkes processes that include self-excitation or inhibition, generalizing previous methods limited to self-excitation only. They implemented a maximum likelihood estimator for an exponential kernel and demonstrated that it provides more accurate estimations than existing approaches in inhibition contexts.
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.