An EM Algorithm for the Time-Variant Vector Hawkes Process

In recent years the Hawkes model has been applied in diverse application areas ranging from neural coding, genomics, econometrics to social networks. In the original Hawkes model, the parameters are time-invariant. But a number of studies indicate the need for time-variant parameters. In this paper, we extend previous work on time-variant scalar Hawkes models to the vector case. In addition, we develop a computational procedure that is exact and so is very fast. We demonstrate the algorithm using some neural data.