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 datasets and a case-study illustrate the performances of the estimation, notably of the reproduction function even when time intervals are relatively large.

翻译：本文为观察不力的线性固定鹰工序提供了一种参数估计方法。当未观察到点的确切位置,而只是计及固定长度的时段时,根据可能性确定的方法是不可行的。我们表明,根据惠特尔方法进行的光谱估计适合这种情况,并提供一致和无症状的正常估测器,但提供复制功能的微小时间条件。模拟数据集和案例研究说明了估计的性能,特别是复制功能,即使时间间隔相对较大。