# Spectral estimation of Hawkes processes from count data

arXiv: https://arxiv.org/abs/2003.04314 · HTML: https://mlsanity.com/paper/2003.04314/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data](https://mlsanity.com/paper/2111.02062/) (2021)
- [Estimation of an Order Book Dependent Hawkes Process for Large Datasets](https://mlsanity.com/paper/2307.09077/) (2023)

## Abstract (arXiv)

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.