## Electronic Journal of Statistics

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

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 13, Number 2 (2019), 3654-3709.

Dates
First available in Project Euclid: 1 October 2019

https://projecteuclid.org/euclid.ejs/1569895285

Digital Object Identifier
doi:10.1214/19-EJS1610

Mathematical Reviews number (MathSciNet)
MR4013748

Zentralblatt MATH identifier
07113728

#### Citation

Hoffmann, Michael; Dette, Holger. On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process. Electron. J. Statist. 13 (2019), no. 2, 3654--3709. doi:10.1214/19-EJS1610. https://projecteuclid.org/euclid.ejs/1569895285

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