Faculty of Actuarial Science & Insurance Seminar with Paul Embrechts

In this talk the Hawkes skeleton and the Hawkes graph are introduced. These objects summarize the branching structure of a multivariate Hawkes point process in a compact, yet meaningful way. I demonstrate how graph-theoretic vocabulary is very convenient for the discussion of multivariate Hawkes processes. I also show how the graph view may be used for the specification and estimation of Hawkes models from large, multitype event streams. We pay special attention to computational issues in the implementation. This makes the results applicable to data with dozens of event streams and thousands of events per component. A simulation study confirms that the presented procedure works as desired. The talk finishes with an application to the modeling of limit order book data in the context of high frequency finance.
The results presented are based on joint work with Matthias Kirchner, RiskLab, ETH Zurich.

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