Multivariate Hawkes processes (MHPs) are versatile probabilistic tools used
to model various real-life phenomena: earthquakes, operations on stock markets,
neuronal activity, virus propagation and many others. In this paper, we focus
on MHPs with exponential decay kernels and estimate connectivity graphs, which
represent the Granger causal relations between their components. We approach
this inference problem by proposing an optimization criterion and model
selection algorithm based on the minimum message length (MML) principle. MML
compares Granger causal models using the Occam's razor principle in the
following way: even when models have a comparable goodness-of-fit to the
observed data, the one generating the most concise explanation of the data is
preferred. While most of the state-of-art methods using lasso-type penalization
tend to overfitting in scenarios with short time horizons, the proposed
MML-based method achieves high F1 scores in these settings. We conduct a
numerical study comparing the proposed algorithm to other related classical and
state-of-art methods, where we achieve the highest F1 scores in specific sparse
graph settings. We illustrate the proposed method also on G7 sovereign bond
data and obtain causal connections, which are in agreement with the expert
knowledge available in the literature.

多元 Hawkes 过程是一种灵活的概率工具，用于对各种现实生活现象进行建模；本文关注指数衰减核的多元 Hawkes 过程，并通过最小信息长度原则提出了一种优化准则和模型选择算法来估计其组成部分之间的 Granger 因果关系的连通性图；通过数值研究，将该方法与其他相关方法进行了比较，在特定的稀疏图设置中获得了最高的 F1 得分；同时，通过对 G7 主权债券数据进行分析，得到了与文献中专家知识一致的因果关系。