使用Fréchet统计量检测多元Hawkes过程中的结构变化
Detecting Structural Shifts in Multivariate Hawkes Processes with Fréchet Statistics
AI总结：
本文提出基于Fréchet统计量的多元Hawkes过程变点检测方法，通过窗口化估计核矩阵并重建符号拉普拉斯矩阵，实验验证其在模拟和加密货币数据上能准确检测因果结构变化。
摘要：
本文提出了一种使用网络的Fréchet统计量进行多元Hawkes过程变点检测的新方法。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来重建符号拉普拉斯矩阵。我们通过在模拟数据集和加密货币数据集上的实验证明了该方法的有效性。我们的结果表明，该方法能够准确检测和刻画多元Hawkes过程中因果结构的变化，并可能在金融和神经科学等领域具有潜在应用。所提出的方法是先前在点过程设置中Fréchet统计量研究的扩展，代表了对多元点过程变点检测领域的重要贡献。
英文摘要：
This paper proposes a new approach for change point detection in multivariate Hawkes processes using Fréchet statistic of a network. The 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 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 Fréchet statistics in point process settings and represents an important contribution to the field of change point detection in multivariate point processes.
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