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 fitting parametric Hawkes models. Our estimation method avoids the a priori assumptions on the model from a straighforward MLE-approach and is numerically more flexible than the latter. Our method has two tuning parameters: one controlling numerical complexity, the other one controlling the sparseness of the estimated graph. A simulation study confirms that the presented procedure works as desired. We pay special attention to computational issues in the implementation. This makes our results applicable to high-dimensional event-stream data, such as dozens of event streams and thousands of events per component.

翻译：本文介绍 Hawkes 和 Hawkes 图表。 这些对象以精密但有意义的方式概括多变量 Hawkes 点进程的分支结构。 我们展示了图形理论词汇( “ 原始设置 ” 、 “ 原始设置 ” 、 “ 连接 ” 、 “行走 ” 、 “行重量 ” 、.) 如何非常方便讨论多变量雕刻过程。 例如, 我们用图表术语来重新配置基于经典的基于egenvale的多类型分支进程的亚临界标准。 除了这些更多的术语贡献外, 我们展示了图表观点如何用于说明和估计来自大型、 多类型事件流的 Hawks 模型的规格和估计。 根据先前的工作, 我们给出了一个非参数性统计程序来估算 Hawkets 骨架和 Hawks 图表 。 我们的估算方法避免了该模型的先前假设性假设性, 从直径向MLE- Approach, 从数字角度看, 并且比后者更灵活。 我们的模型的模拟性估算性估算性计算结果, 我们的两种模型的计算方法, 用于控制高位数分析性计算结果, 。 我们的计算结果的计算, 用于分析性研究, 用于控制其他的计算, 我们的计算结果, 的计算结果, 用于控制高位数式的计算, 的计算, 我们的计算, 的计算。