Estimation, diagnostics, and extensions of nonparametric Hawkes processes

Abstract

The Hawkes self-exciting model has become one of the most popular point-process models in many research areas in the natural and social sciences because of its capacity for investigating the clustering effect and positive interactions among individual events/particles. This article discusses a general nonparametric framework for the estimation, extensions, and post-estimation diagnostics of Hawkes models, which can be divided into 4 steps:

1. Model design. Design the model according to the features of the observation data, specifically the particular mathematical form of the Hawkes model (parametric, nonparametric, or semiparametric), which depend on the available empirical knowledge of the studied process.

2. Estimation design. Design the estimation according to the types of model formation, use the MLE method or the EM algorithm to estimate parametric model, and use stochastic reconstruction to reconstruct the nonparametric components.

3. Improvement. Improve the estimation using kernel estimates or the Bayesian method.

4. Diagnosing the new model. The reconstruction method can be naturally used as a diagnostic tool to check whether it is possible to improve the model or not.

Lecture recording is available here.