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Article Dans Une Revue Annals of Statistics Année : 2022

Spectral estimation of Hawkes processes from count data

Résumé

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.
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Dates et versions

hal-03718823 , version 1 (09-07-2022)

Identifiants

Citer

Felix Cheysson, Gabriel Lang. Spectral estimation of Hawkes processes from count data. Annals of Statistics, 2022, 50 (3), pp.1722-1746. ⟨10.1214/22-aos2173⟩. ⟨hal-03718823⟩
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