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The local fractional bootstrap

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Title: The local fractional bootstrap
Authors: Bennedsen, M
Hounyo, U
Lunde, A
Pakkanen, MS
Item Type: Journal Article
Abstract: We introduce a bootstrap procedure for high‐frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our new resampling method, the local fractional bootstrap, relies on simulating an auxiliary fractional Brownian motion that mimics the fine properties of high‐frequency differences of the Brownian semistationary process under the null hypothesis. We prove the first‐order validity of the bootstrap method, and in simulations, we observe that the bootstrap‐based hypothesis test provides considerable finite‐sample improvements over an existing test that is based on a central limit theorem. This is important when studying the roughness properties of time series data. We illustrate this by applying the bootstrap method to two empirical data sets: We assess the roughness of a time series of high‐frequency asset prices and we test the validity of Kolmogorov's scaling law in atmospheric turbulence data.
Issue Date: Mar-2019
Date of Acceptance: 24-Jul-2018
URI: http://hdl.handle.net/10044/1/62897
DOI: https://doi.org/10.1111/sjos.12355
ISSN: 0303-6898
Publisher: Wiley
Start Page: 329
End Page: 359
Journal / Book Title: Scandinavian Journal of Statistics
Volume: 46
Issue: 1
Copyright Statement: © 2018 Board of the Foundation of the Scandinavian Journal of Statistics. This is the accepted version of the following article: Bennedsen, M, Hounyo, U, Lunde, A, Pakkanen, MS. The local fractional bootstrap. Scand J Statist. 2019; 46: 329– 359, which has been published in final form at https://doi.org/10.1111/sjos.12355
Sponsor/Funder: Academy of Finland
Funder's Grant Number: 258042
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
bootstrap
Brownian semistationary process
fractional Brownian motion
Holder regularity
roughness
stochastic volatility
turbulence
BROWNIAN SEMISTATIONARY PROCESSES
VOLATILITY
ESTIMATORS
PRICES
math.ST
math.ST
q-fin.ST
stat.TH
60G10, 60G15, 60G17, 60G22, 62M07, 62M09, 65C05
math.ST
math.ST
q-fin.ST
stat.TH
60G10, 60G15, 60G17, 60G22, 62M07, 62M09, 65C05
Statistics & Probability
0104 Statistics
Publication Status: Published
Online Publication Date: 2018-09-26
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences