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 processes has been missing in the literature. In this work, we establish a bootstrap-based goodness-of-fit test which 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.

翻译：尽管参数化点过程在理论和应用中广泛使用，但文献中一直缺乏一种可靠的拟合优度检验方法，用于判断给定参数模型是否适用于自激励点过程产生的数据。本研究建立了一种基于自助法的拟合优度检验方法，该方法经验证适用于各类自激励点过程（甚至更广泛的场景）。在填充渐近框架下，我们证明了该检验的渐近一致性，但仅限于基础点过程为非齐次泊松过程的特定情形。