SPECTRAL ESTIMATION OF HAWKES PROCESSES FROM COUNT DATA

• 成果类型: Article
• 署名作者: Cheysson, Felix; Lang, Gabriel
• 署名单位: INRAE; Universite Paris Saclay; AgroParisTech
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2173
• 发表日期: 2022
• 页码: 1722-1746
• 关键词: CENTRAL-LIMIT-THEOREM; point-processes; time; models

摘要

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.