Estimation of self-exciting point processes from time-censored data

Self-exciting point processes, widely used to model arrival phenomena in nature and society, are often difficult to identify. The estimation becomes even more challenging when arrivals are recorded only as bin counts on a finite partition of the observation interval. In this paper, we propose the recursive identification with sample correction (RISC) algorithm for the estimation of process parameters from time-censored data. In every iteration, a synthetic sample path is generated and corrected to match the observed bin counts. Then the process parameters update and a unique iteration is performed to successively approximate the stochastic characteristics of the observed process. In terms of finite-sample approximation error, the proposed RISC framework performs favorably over extant methods, as well as compared to a naïve locally uniform sample redistribution. The results of an extensive numerical experiment indicate that the reconstruction of an intrabin history based on the conditional intensity of the process is crucial for attaining superior performance in terms of estimation error.