Bootstrap inference for Hawkes and general point processes

Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihood-based estimators tests. As an alternative, to improve finite sample performance, this paper considers bootstrap-based inference interval estimation testing. Specifically, a wide class of we consider novel bootstrap scheme labeled ‘fixed intensity bootstrap’ (FIB), where conditional kept fixed across repetitions. The FIB, which very simple implement fast practice, extends previous ideas from literature time series discrete time, so-called design’ volatility’ schemes have shown be particularly useful effective. We compare FIB with classic recursive bootstrap, here ‘recursive (RIB). In RIB algorithms, stochastic world implementation more involved, due its sequential structure. For both schemes, provide new (asymptotic) theory allows assess validity, propose ‘non-parametric’ approach resampling time-changed transformations original waiting times. also establish link between proposed bootstraps related autoregressive duration (ACD) models. Lastly, show effectiveness different samples through set detailed Monte Carlo experiments, applications financial data social media illustrate methodology.