Hawkes graphs
Paul Embrechts, Matthias Kirchner

TL;DR
This paper introduces the Hawkes skeleton and Hawkes graph to summarize multivariate Hawkes processes, providing a graph-theoretic framework for model specification, estimation, and analysis, especially suited for high-dimensional data.
Contribution
It presents a novel graph-based representation of Hawkes processes and a nonparametric estimation method that is flexible and scalable for large multitype event streams.
Findings
Effective nonparametric estimation of Hawkes graphs demonstrated
Method handles high-dimensional, large-scale event data
Graph-based approach improves model specification and interpretation
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 graph-theoretic vocabulary (`ancestor sets', `parent sets', `connectivity', `walks', `walk weights', ...) 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 may 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 may then be used for specifying and…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPoint processes and geometric inequalities · Diffusion and Search Dynamics · Toxic Organic Pollutants Impact
