Estimating Jump Activity Using Multipower Variation

Research output: Contribution to journalArticlepeer-review


Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for infer- ence in pure-jump models. This article 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 article undertakes a nonparametric analysis of the jump activity of bitcoin and shows that bitcoin is a pure jump process with high jump activity, which is critically different from conventional currencies that include a Brownian motion component.

Bibliographical metadata

Original languageEnglish
JournalJournal of Business and Economic Statistics
Early online date25 Jun 2020
Publication statusE-pub ahead of print - 25 Jun 2020