Functional Marked Hawkes Processes, with a View to Model Hurricanes Data

Abstract

While statistical methods and models for spatial point processes with scalar marks are rather well-established, their counterparts for functional marked spatio-temporal point processes remain in their infancy. As a result, this has become a growing research topic, driven by advances in data collection, storage, and availability. Representative instances include earthquake and hurricane data, which involve functional marks and exhibit self-exciting behaviour. We contribute to this emerging area by developing a marked functional Hawkes point process and applying the proposed model to analyse hurricane data in the Atlantic Basin.