Estimating the degree of activity of jumps in high frequency data

TL;DR

This paper introduces a new index for jump activity in high-frequency financial data, proposes estimators for it, and demonstrates their effectiveness in identifying infinite activity jumps despite Brownian volatility.

Contribution

It develops a generalized jump activity index and estimators that work with discretely sampled data, even with Brownian volatility present.

Findings

Evidence of infinitely active jumps in stock returns

Successful estimation of jump activity index

Method remains effective despite Brownian volatility

Abstract

We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.