Estimating Jump Activity Using Multipower Variation

Bibliographic Data

ID19418358
AuthorsAleksey Kolokolov (0009-0005-3512-4366, Alliance Manchester Business School, The University of Manchester, Manchester, UK, corresponding author)
Year2022
Volume40
Issue1
Pages128-140
Publication date2022-01-02
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueJournal of Business and Economic Statistics (JOURNAL)
Journal identifiersISSN: 0735-0015 • E-ISSN: 1537-2707
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/07350015.2020.1784745
OpenAlexW3036998411
LanguageEN
Citations received1
References cited36

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

Brownian motion · Econometrics · Estimator · Inference · Jump · Jump diffusion · Jump process · Martingale (probability theory) · Nonparametric statistics · Physics · Semimartingale · Statistical physics · Statistics · Complex Systems and Time Series Analysis · Computer Science · Financial Risk and Volatility Modeling · Mathematics · Stochastic processes and financial applications · Applied Mathematics · Artificial Intelligence

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