Estimating Jump Activity Using Multipower Variation

Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference in pure-jump models. The paper shows how to build a simple and precise estimator of the jump activity index of a semimartingale observed at a high frequency by comparing different multipowers. The novel methodology allows to infer whether a discretely observed process contains a continuous martingale component. The empirical part of the paper undertakes a nonparametric analysis of jump activity of bitcoin. The implementation of the new jump activity estimator indicates that bitcoin is a pure jump process with high jump activity, which is critically different from conventional currencies that include a Brownian motion component