Hoffmann, MichaelVetter, MathiasDette, Holger2016-10-102016-10-102016http://hdl.handle.net/2003/3523310.17877/DE290R-17276In 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.enDiscussion Paper / SFB823;49, 2016Levy measuregradual changesweak convergenceempirical processes310330620working paper