Spectral estimation of Hawkes processes from count data
针对仅观测到固定时间区间内计数、而非精确事件时间的线性平稳霍克斯过程，提出基于Whittle方法的谱估计，给出相合且渐近正态的估计量，并通过模拟和案例验证性能。
This paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood are not feasible. We show that spectral estimation based on Whittle’s method is adapted to this case and provides consistent and asymptotically normal estimators, provided a mild moment condition on the reproduction function. Simulated data sets and a case-study illustrate the performances of the estimation, notably of the reproduction function even when time intervals are relatively large.