## Bernoulli

- Bernoulli
- Volume 23, Number 2 (2017), 1335-1364.

### Nonparametric tests for detecting breaks in the jump behaviour of a time-continuous process

Axel Bücher, Michael Hoffmann, Mathias Vetter, and Holger Dette

#### Abstract

This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain test statistics for breaks in the jump measure of an Itô semimartingale are constructed. Whenever limiting distributions depend in a complicated way on the unknown jump measure, empirical quantiles are obtained using a multiplier bootstrap scheme. An extensive simulation study shows a good performance of our tests in finite samples.

#### Article information

**Source**

Bernoulli, Volume 23, Number 2 (2017), 1335-1364.

**Dates**

Received: December 2014

Revised: September 2015

First available in Project Euclid: 4 February 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1486177401

**Digital Object Identifier**

doi:10.3150/15-BEJ780

**Mathematical Reviews number (MathSciNet)**

MR3606768

**Zentralblatt MATH identifier**

06701628

**Keywords**

change points Lévy measure multiplier bootstrap sequential empirical processes weak convergence

#### Citation

Bücher, Axel; Hoffmann, Michael; Vetter, Mathias; Dette, Holger. Nonparametric tests for detecting breaks in the jump behaviour of a time-continuous process. Bernoulli 23 (2017), no. 2, 1335--1364. doi:10.3150/15-BEJ780. https://projecteuclid.org/euclid.bj/1486177401