Hawkes-laguerre reduced rank model for point processes

In recent years there has been a surge in the demand for analysis tools for multivariate point process data driven by work in neural coding and high frequency finance. In both these areas data volumes have become huge but few dimension reduction methods have been developed. Here we introduce a reduced rank model for the multivariate point process and provide a maximum likelihood estimator which we compute by an NMF type algorithm. However, the dependence on the point process history in the model implies our algorithm does not fit the traditional framework. The method is illustrated with a simulation and some data from cortical recordings from cats.