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.
|Journal||Journal of Business and Economic Statistics|
|Early online date||25 Jun 2020|
|Publication status||E-pub ahead of print - 25 Jun 2020|
- Jump activity
- Multipower variation
- High-frequency data