In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection and fitting, and in volatility estimation. In this paper, we give a novel estimate of the jump activity, together with corresponding confidence intervals. Our estimate improves upon previous work, achieving near-optimal rates of convergence, and good finite-sample performance in Monte-Carlo experiments.
Adam D. Bull. "Near-optimal estimation of jump activity in semimartingales." Ann. Statist. 44 (1) 58 - 86, February 2016. https://doi.org/10.1214/15-AOS1349