Estimating Jump Activity Using Multipower Variation

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


  • bitcoin
  • Jump activity
  • Multipower variation
  • High-frequency data
  • Jumps


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