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In applications the properties of a stochastic feature often change graduallyrather than abruptly, that is: after a constant phase for some time they slowlystart to vary. In this paper we discuss statistical inference for the detectionand the localisation of gradual changes in the jump characteristic of adiscretely observed Ito semimartingale. We propose a new measure of timevariation for the jump behaviour of the process. The statistical uncertainty ofa corresponding estimate is analyzed by deriving new results on the weakconvergence of a sequential empirical tail integral process and a correspondingmultiplier bootstrap procedure.

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