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

TL;DR

This paper develops new statistical tests and estimation methods for detecting both abrupt and gradual changes in the jump behavior of Ito semimartingales, accommodating jumps of any size, with validation through simulations.

Contribution

It introduces procedures analyzing jumps of arbitrary size in Ito processes, extending existing methods that require minimum jump heights.

Findings

Tests effectively detect changes in jump behavior.

Bootstrap approach provides reliable critical values.

Simulation confirms good finite-sample performance.

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.