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.
"Estimating the degree of activity of jumps in high frequency data." Ann. Statist. 37 (5A) 2202 - 2244, October 2009. https://doi.org/10.1214/08-AOS640