Switched Hawkes Processes

Hawkes processes are a class of auto-regressive point processes that are commonly used in modeling data in which events tend to cluster and influence the likelihood of future events. Because of their ability to model and explain how events or processes can influence each other, Hawkes processes (and their multivariate extensions) have been applied in a variety of practical applications such as analyzing financial time series, communication networks, and biological networks, to name just a few. In practice, the dynamics of such systems often depend on external factors that may change over time and that may drive different kinds of behavior. In this paper, we consider a switched Hawkes process which can be used to model systems in which the parameters of the process dynamically change depending on some (known) external state. We propose a simple maximum likelihood estimation approach which we validate using synthetic simulations. We then apply our model to a real-world traffic sensor dataset to study traffic patterns during different configurations of the traffic lights at an intersection.