Abstract

Locally stationary Hawkes processes were introduced as a generalisation to the classical Hawkes processes introduced in 1971. Hawkes processes are a class of point processes with a self-exciting structure. The locally stationary extension allowed for a time-varying second-order structure which has many applications in the physical sciences and finance. These generalisations, while useful, are relatively new to the literature. There is limited discussion on estimation methods for the time-varying parameters in these processes which has so far only focused on estimating the whole function and not the individual parameter functions. This research introduces a method of inference for the time-varying background intensity of the Hawkes process. This estimation method can be utilised for any kernel choice for the class of self-exciting point processes. Furthermore, the estimation procedure allows for the time-varying background intensity to be any continuous function.

Andrew Connell

Graduate Mathematician & Statistician

My research interests include signal processing, time series analysis and point processes.