Nonparametric estimation of locally stationary Hawkes processe

TL;DR

This paper develops a nonparametric estimation method for multivariate locally stationary Hawkes processes with time-varying baseline hazards and kernels, extending stationary process theory to a more flexible, time-dependent setting.

Contribution

It introduces a localized estimation approach for time-dependent parameters in multivariate Hawkes processes, extending existing stationary process theory.

Findings

Asymptotic properties of the estimators are established.

The method effectively captures time-varying dynamics.

Theoretical extension from stationary to locally stationary processes.

Abstract

In this paper we consider multivariate Hawkes processes with baseline hazard and kernel functions that depend on time. This defines a class of locally stationary processes. We discuss estimation of the time-dependent baseline hazard and kernel functions based on a localized criterion. Theory on stationary Hawkes processes is extended to develop asymptotic theory for the estimator in the locally stationary model.