Hawkes-Laguerre dynamic index models for point processes

The availability of multivariate point process data in a number of application areas such as neural coding and stochastic finance is generating demand for analysis tools for handling such high-dimensional data. Existing models suffer from the curse of dimensionality problem and are not applicable in the high-dimensional setting. In this paper, we introduce a dynamic index model for the multivariate point process and provide a maximum likelihood estimator which we compute by a non-negative matrix factorization (NMF)-type algorithm. However, the dependence on the point process history in the model implies our algorithm does not fit the traditional NMF framework. The method is illustrated with some data from cortical recordings in cats.