Vector Nonlinear Hawkes Model with Inhibition

The Hawkes process has been applied successfully to model point process data in a number of application areas including seismology, neural coding, high-frequency finance, and genomics. But the Hawkes process does not accommodate inhibitory effects observed jointly with excitatory behavior, e.g., for regulating neural activity in the brain and binding of transcriptional factors along a genome. In this paper, we extend our previous work on modeling inhibitory effects in a scalar point process to develop a nonlinear Hawkes model for the vector case. We develop a maximum likelihood procedure for the vector point process and demonstrate the algorithm using some neural and genomic data. A comparison with the multivariate linear Hawkes model shows the superiority of the proposed model.