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The Local Fractional Bootstrap

Mikkel Bennedsen (), Ulrich Hounyo (), Asger Lunde () and Mikko S. Pakkanen ()
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Mikkel Bennedsen: Aarhus University and CREATES, Postal: Department of Economics and Business Economics, Fuglesangs Allé 4, 8210 Aarhus V, Denmark
Ulrich Hounyo: Aarhus University and CREATES, Postal: Department of Economics and Business Economics, Fuglesangs Allé 4, 8210 Aarhus V, Denmark
Asger Lunde: Aarhus University and CREATES, Postal: Department of Economics and Business Economics, Fuglesangs Allé 4, 8210 Aarhus V, Denmark
Mikko S. Pakkanen: Imperial College London and CREATES, Postal: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: Brownian semistationary process; roughness; fractal index; Hölder regularity; fractional Brownian motion; bootstrap; stochastic volatility; turbulence JEL Classification: C12, C22, C63, G12 MSC 2010 Classification: 60G10, 60G15, 60G17, 60G22, 62M07, 62M09, 65C05 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets
Date: 2016-05-03
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