On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process
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Date
2018
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Abstract
This paper introduces test and estimation procedures for abrupt and gradual changes in
the entire jump behaviour of a discretely observed Ito 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 Ito 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.
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Keywords
Lévy measure, gradual changes, change points, multiplier bootstrap, weak convergence, empirical processes, transition kernel, jump compensator