  It is often assumed that events cannot occur simultaneously when modelling
data with point processes. This raises a problem as real-world data often
contains synchronous observations due to aggregation or rounding, resulting
from limitations on recording capabilities and the expense of storing high
volumes of precise data. In order to gain a better understanding of the
relationships between processes, we consider modelling the aggregated event
data using multivariate Hawkes processes, which offer a description of
mutually-exciting behaviour and have found wide applications in areas including
seismology and finance. Here we generalise existing methodology on parameter
estimation of univariate aggregated Hawkes processes to the multivariate case
using a Monte Carlo Expectation Maximization (MC-EM) algorithm and through a
simulation study illustrate that alternative approaches to this problem can be
severely biased, with the multivariate MC-EM method outperforming them in terms
of MSE in all considered cases.
