Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

Abstract

In applications changes of the properties of a stochastic feature occur often gradually rather than abruptly, that is: after a constant phase for some time they slowly start to change. Efficient analysis for change points should address the specific features of such a smooth change. In this paper we discuss statistical inference for localizing and detecting gradual changes in the jump characteristic of a discretely observed Ito semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analyzed deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure.