RESEARCH ARTICLE A Nonparametric EM algorithm for Multiscale Hawkes Processes

Estimating the conditional intensity of a self-exciting point process is particularly challenging when both exogenous and endogenous e!ects play a role in clustering. We propose maximum penalized likelihood estimation as a method for simultaneously estimating the background rate and the triggering density of Hawkes process intensities that vary over multiple time scales. We compare the accuracy of the algorithm with the recently introduced Model Independent Stochastic Declustering (MISD) algorithm and then use the model to examine self-excitation in Iraq IED event patterns.

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