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Estimating Jump Activity Using Multipower Variation

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  • Aleksey Kolokolov

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.

Suggested Citation

  • Aleksey Kolokolov, 2022. "Estimating Jump Activity Using Multipower Variation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 128-140, January.
    • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:1:p:128-140
    DOI: 10.1080/07350015.2020.1784745
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    Cited by:

    1. Zhang, Chuanhai & Zhang, Zhengjun & Xu, Mengyu & Peng, Zhe, 2023. "Good and bad self-excitation: Asymmetric self-exciting jumps in Bitcoin returns," Economic Modelling, Elsevier, vol. 119(C).

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