Statistica Sinica 23 (2013),

THE STATISTICAL ANALYSIS OF SELF-EXCITING

POINT PROCESSES

Kai Kopperschmidt and Winfried Stute

The Nielsen Company $($Germany$)$ GmbH and University of Giessen

Abstract: In this paper we study minimum distance estimation for self-exciting point processes. These processes allow for a flexible semi-parametric modeling of the compensator. As a main result, we show the strong consistency and asymptotic normality of our estimator. We also present an application to a data set from micro-economics.

Key words and phrases: Asymptotic normality, consistency, market research, self-exciting point processes.