This paper proposes a new approach for change point detection in causal networks of multivariate Hawkes processes using Frechet statistics. Our method splits the point process into overlapping windows, estimates kernel matrices in each window, and reconstructs the signed Laplacians by treating the kernel matrices as the adjacency matrices of the causal network. We demonstrate the effectiveness of our method through experiments on both simulated and real-world cryptocurrency datasets. Our results show that our method is capable of accurately detecting and characterizing changes in the causal structure of multivariate Hawkes processes, and may have potential applications in fields such as finance and neuroscience. The proposed method is an extension of previous work on Frechet statistics in point process settings and represents an important contribution to the field of change point detection in multivariate point processes.

翻译：本文提出了一种利用Fréchet统计量在多元霍克斯过程因果网络中检测变点的新方法。该方法将点过程分割为重叠窗口，在每个窗口中估计核矩阵，并通过将核矩阵视为因果网络的邻接矩阵重构符号拉普拉斯矩阵。我们通过模拟实验和真实加密货币数据集实验验证了方法的有效性。结果表明，该方法能够准确检测并表征多元霍克斯过程因果结构的变化，在金融和神经科学等领域具有潜在应用价值。所提方法是对点过程中Fréchet统计量先前研究的扩展，为多元点过程变点检测领域作出了重要贡献。