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2019 On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process
Michael Hoffmann, Holger Dette
Electron. J. Statist. 13(2): 3654-3709 (2019). DOI: 10.1214/19-EJS1610

Abstract

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.

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Michael Hoffmann. Holger Dette. "On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process." Electron. J. Statist. 13 (2) 3654 - 3709, 2019. https://doi.org/10.1214/19-EJS1610

Information

Received: 1 February 2018; Published: 2019
First available in Project Euclid: 1 October 2019

zbMATH: 07113728
MathSciNet: MR4013748
Digital Object Identifier: 10.1214/19-EJS1610

Subjects:
Primary: 60F17 , 60G51 , 62G10 , 62M99

Keywords: Change points , Empirical processes , gradual changes , jump compensator , Lévy measure , multiplier bootstrap , transition kernel , weak convergence

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Vol.13 • No. 2 • 2019
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