B0698
Title: Neural network estimation of partially observed Hawkes processes
Authors: Ioane Muni Toke - CentraleSupelec (France) [presenting]
Abstract: Hawkes processes are very popular in many fields, such as biology, seismology or finance. In the standard case of fully observed event times, maximum-likelihood estimation is possible (although at a high computational cost in the case of non-exponential excitation kernels). In many applications, however, event times are only partially observed. In high-frequency finance, for example, multiple events may occur within one millisecond or a fraction of a millisecond, and one may observe several events at the same time or within the same time interval. Several methods have been recently developed in order to estimate Hawkes processes using datasets with partially observed event times, sometimes called aggregated Hawkes data, bin count Hawkes data or time-censored Hawkes data. A prior study approximates the Hawkes process with an INAR (integer-valued auto-regressive) to develop an estimation method for bin count data. A recent study adapted an EM algorithm to the partially observed case. Another study computes a Whittle log-likelihood of the aggregated process and builds a spectral estimation method. Supervised learning methods are tested with recurrent neural networks in order to estimate partially observed Hawkes processes. Extensive computational tests are provided, to analyze the performances for several excitation kernels and compare the results to the methods mentioned above.
