DETECTING ABRUPT CHANGES IN HIGH-DIMENSIONAL SELF-EXCITING POISSON PROCESSES

Abstract

High-dimensional self-exciting point processes are widely used to model discrete event data in which past and current events affect the likelihood of future events. In this study, we detect abrupt changes in the coefficient matrices of discrete-time high-dimensional self-exciting Poisson processes, which have yet to be studied because of the theoretical and computational challenges in the nonstationary and high-dimensional nature of the underlying process. We propose a penalized dynamic programming approach, supported by a theoretical rate analysis and numerical evidence.