Nonparametric estimation of variable productivity Hawkes processes

Frederic P. Schoenberg

Under Review February 28, 2021, SCEC Contribution #10935

An extension of the Hawkes model is considered where the productivity is variable. In particular, the case is explored where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood estimators of these productivities. This estimator is compared with an empirical estimator and ways are explored of stabilizing both estimators by lower truncating, smoothing, and rescaling the estimates. Properties of the estimators are explored in simulations, and the methods are applied to seismological and epidemic datasets to show and
quantify substantial variation in productivity.

Key Words
Point process, Hawkes process, self-exciting point process, non-parametric estimation, earthquakes, Chlamydial infection

Schoenberg, F. P. (2021). Nonparametric estimation of variable productivity Hawkes processes. Journal of Time Series Analysis, (under review).