  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.
