Title: Nonparametric estimation of locally stationary Hawkes processe,
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.