Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes
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Date
2016
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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.
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Keywords
Levy measure, gradual changes, weak convergence, empirical processes