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

TL;DR

This paper develops nonparametric tests to detect changes in the jump behavior of continuous-time stochastic processes, utilizing empirical tail integrals and bootstrap methods for complex distributions.

Contribution

It introduces new nonparametric tests for jump measure changes in Ito semimartingales, with asymptotic theory and bootstrap calibration for practical application.

Findings

Tests perform well in finite samples

Bootstrap scheme effectively handles unknown jump measures

Asymptotic distributions derived for test statistics

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 tests statistics for breaks in the jump measure of an Ito 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.