Abstract

The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time stamps and marks. However, available data are often rounded or aggregated. We develop a Bayesian estimation procedure for the parameters of a Hawkes process based on aggregated data. Our approach is developed for temporal, spatio-temporal, and mutually exciting Hawkes processes where data are available over discrete time periods and regions. The method is demonstrated on simulated temporal and spatio-temporal data in the presence of one or more interacting processes, and under varying coarseness of data aggregation. Finally, we analyze spatio-temporal point pattern data of insurgent attacks in Iraq from October to December 2006, and we find coherent results across different time and space aggregations.