Modeling Event Dynamics by Self-Exciting Processes with Random Memory

TL;DR

This paper introduces an extended Hawkes process model with random self-excitation duration to better capture the transient self-excitation effects in event data, demonstrated through sports analytics and adaptable to other fields.

Contribution

The paper develops a novel Hawkes process extension incorporating random self-excitation duration, with estimation procedures and simulation algorithms, applicable across various research domains.

Findings

Successfully modeled sports event data with the new process

Demonstrated the model's flexibility in different fields

Provided algorithms for simulation and parameter estimation

Abstract

Event history data from sports competitions have recently drawn increasing attention in sports analytics to generate data-driven strategies. Such data often exhibit self-excitation in the event occurrence and dependence within event clusters. The conventional event models based on gap times may struggle to capture those features. In particular, while consecutive events may occur within a short timeframe, the self-excitation effect caused by previous events is often transient and continues for a period of uncertain time. This paper introduces an extended Hawkes process model with random self-excitation duration to formulate the dynamics of event occurrence. We present examples of the proposed model and procedures for estimating the associated model parameters. We employ the collection of the corner kicks in the games of the 2019 regular season of the Chinese Super League to motivate and illustrate the modeling and its usefulness. We also design algorithms for simulating the event process under proposed models. The proposed approach can be adapted with little modification in many other research fields such as Criminology and Infectious Disease.