# A Monte Carlo EM Algorithm for the Parameter Estimation of Aggregated Hawkes Processes

arXiv: https://arxiv.org/abs/2001.07160 · HTML: https://mlsanity.com/paper/2001.07160/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2020.

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

- [Interval-censored Hawkes processes](https://mlsanity.com/paper/2104.07932/) (2021)
- [Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data](https://mlsanity.com/paper/2111.02062/) (2021)

## Abstract (arXiv)

A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical limits on the accuracy of measurements, aggregated data is common. In order to use point processes to model such event data, tools for handling parameter estimation are essential. Here we consider parameter estimation of the Hawkes process, a type of self-exciting point process that has found application in the modeling of financial stock markets, earthquakes and social media cascades. We develop a novel optimization approach to parameter estimation of aggregated Hawkes processes using a Monte Carlo Expectation-Maximization (MC-EM) algorithm. Through a detailed simulation study, we demonstrate that existing methods are capable of producing severely biased and highly variable parameter estimates and that our novel MC-EM method significantly outperforms them in all studied circumstances. These results highlight the importance of correct handling of aggregated data.