Nonparametric estimation of variable productivity Hawkes processes

Frederic Paik Schoenberg

Environmetrics, 2022, vol. 33, issue 6

Abstract: Hawkes models are frequently used to describe point processes that are clustered spatial‐temporally, and have been used in numerous applications including the study of earthquakes, invasive species, and contagious diseases. 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.

Date: 2022
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