Nonparametric estimation of locally stationary Hawkes processes - Mammen, Enno; Müller, Marilena (Bernoulli, 2023)
In this paper we consider multivariate Hawkes processes with baseline conditional intensities and reproduction functions that depend on time. This defines a class of locally stationary processes. We discuss estimation of the time-dependent baseline intensities and reproduction 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.