The null hypothesis of common jumps in case of irregular and asynchronous observations

TL;DR

This paper introduces new statistical tests for detecting jumps and common jumps in financial data modeled as semimartingales, using irregular and asynchronous observations, with improved finite sample performance.

Contribution

It develops novel ratio-based tests for jumps and common jumps in semimartingales, including central limit theorems and bootstrap methods for irregular, asynchronous data.

Findings

Corrected statistics improve finite sample performance.

Tests outperform existing methods with regular observations.

Bootstrap procedures effectively assess limiting distributions.

Abstract

This paper proposes novel tests for the absence of jumps in a univariate semimartingale and for the absence of common jumps in a bivariate semimartingale. Our methods rely on ratio statistics of power variations based on irregular observations, sampled at different frequencies. We develop central limit theorems for the statistics under the respective null hypotheses and apply bootstrap procedures to assess the limiting distributions. Further we define corrected statistics to improve the finite sample performance. Simulations show that the test based on our corrected statistic yields good results and even outperforms existing tests in the case of regular observations.