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On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process. (English) Zbl 1466.60070

Summary: This paper introduces test and estimation procedures for abrupt and gradual changes in the entire jump behaviour of a discretely observed Itō semimartingale. In contrast to existing work we analyse jumps of arbitrary size which are not restricted to a minimum height. Our methods are based on weak convergence of a truncated sequential empirical distribution function of the jump characteristic of the underlying Itō semimartingale. Critical values for the new tests are obtained by a multiplier bootstrap approach and we investigate the performance of the tests also under local alternatives. An extensive simulation study shows the finite-sample properties of the new procedures.

MSC:

60F17 Functional limit theorems; invariance principles
60G51 Processes with independent increments; Lévy processes
62G10 Nonparametric hypothesis testing
62M99 Inference from stochastic processes
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