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arXiv · 1609.06831

Hawkes Processes with Stochastic Excitations

Young Lee·Kar Wai Lim·Cheng Soon Ong
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Abstract

We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.

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Young Lee, Kar Wai Lim, Cheng Soon Ong. 2016-09-22. Hawkes Processes with Stochastic Excitations. https://arxiv.org/abs/1609.06831

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