Testing whether jumps have finite or infinite activity

TL;DR

This paper develops statistical tests to determine whether jumps in high-frequency financial data are of finite or infinite activity, providing tools to better understand jump behavior in semimartingales.

Contribution

It introduces two symmetric tests for jump activity classification, applicable under high-frequency observations, and demonstrates their effectiveness on stock return data.

Findings

Both tests indicate the presence of infinite-activity jumps in stock returns.

The methods are applicable for high-frequency financial data analysis.

The tests can be used with either null hypothesis, finite or infinite activity.

Abstract

We propose statistical tests to discriminate between the finite and infinite activity of jumps in a semimartingale discretely observed at high frequency. The two statistics allow for a symmetric treatment of the problem: we can either take the null hypothesis to be finite activity, or infinite activity. When implemented on high-frequency stock returns, both tests point toward the presence of infinite-activity jumps in the data.