Spectral estimation of Hawkes processes from count data

Understand

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.