On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process

Hoffmann, M. and Dette, H.

Volume: 13 Pages: 3654-3709
DOI: 10.1214/19-EJS1610
Published: 2019

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. © 2019, Institute of Mathematical Statistics. All rights reserved.

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