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@article{Bennedsen:2019:10.1111/sjos.12355,
author = {Bennedsen, M and Hounyo, U and Lunde, A and Pakkanen, MS},
doi = {10.1111/sjos.12355},
journal = {Scandinavian Journal of Statistics},
pages = {329--359},
title = {The local fractional bootstrap},
url = {http://dx.doi.org/10.1111/sjos.12355},
volume = {46},
year = {2019}
}

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TY  - JOUR
AB  - <jats:title>Abstract</jats:title><jats:p>We introduce a bootstrap procedure for highfrequency 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 highfrequency differences of the Brownian semistationary process under the null hypothesis. We prove the firstorder validity of the bootstrap method, and in simulations, we observe that the bootstrapbased hypothesis test provides considerable finitesample 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 highfrequency asset prices and we test the validity of Kolmogorov's scaling law in atmospheric turbulence data.</jats:p>
AU  - Bennedsen,M
AU  - Hounyo,U
AU  - Lunde,A
AU  - Pakkanen,MS
DO  - 10.1111/sjos.12355
EP  - 359
PY  - 2019///
SN  - 0303-6898
SP  - 329
TI  - The local fractional bootstrap
T2  - Scandinavian Journal of Statistics
UR  - http://dx.doi.org/10.1111/sjos.12355
UR  - http://hdl.handle.net/10044/1/62897
VL  - 46
ER  -

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