Estimating Jump Activity Using Multipower Variation
69 Pages Posted: 12 Jul 2018 Last revised: 15 Dec 2020
Date Written: June 20, 2018
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.
Keywords: Jump Activity, Bitcoin, Jumps, Multipower Variation, High-Frequency Data
JEL Classification: C58, C01, G10
Suggested Citation: Suggested Citation