Hawkes Graphs

Authors:
  • PEP. Embrechts
    P. Embrechts
  • MKM. Kirchner
    M. Kirchner
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Abstract
This paper introduces the Hawkes skeleton and the Hawkes graph. These objects summarize the branching structure of a multivariate Hawkes point process in a compact, yet meaningful way. We demonstrate how the graph-theoretic vocabulary (ancestor sets, parent sets, connectivity, walks, walk weights, etc.) is very convenient for the discussion of multivariate Hawkes processes. For example, we reformulate the classic eigenvalue-based subcriticality criterion of multitype branching processes in graph terms. Next to these more terminological contributions, we show how the graph view can be used for the specification and estimation of Hawkes models from large, multitype event streams. Based on earlier work, we give a nonparametric statistical procedure to estimate the Hawkes skeleton and the Hawkes graph from data. We show how the graph estimation can then be used for specifying and fitting parametric Hawkes models. Our estimation method avoids the a priori assumptions on the model from a straightforward MLE-app...

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