On goodness‐of‐fit testing for self‐exciting point processes
针对自激点过程，提出了一种基于自助法的拟合优度检验方法，用于判断给定参数模型是否适合数据，并在渐近理论上证明了其一致性。
Abstract Despite the wide usage of parametric point processes in theory and applications, a sound goodness‐of‐fit procedure to test whether a given parametric model is appropriate for data coming from a self‐exciting point process has been missing in the literature. In this work, we establish a bootstrap‐based goodness‐of‐fit test that empirically works for all kinds of self‐exciting point processes (and even beyond). In an infill‐asymptotic setting, we also prove its asymptotic consistency, albeit only in the particular case that the underlying point process is inhomogeneous Poisson.