Estimating Jump Activity Using Multipower Variation

Aleksey Kolokolov

Journal of Business & Economic Statistics, 2022, vol. 40, issue 1, 128-140

Abstract: Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference 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.

Date: 2022
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DOI: 10.1080/07350015.2020.1784745

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