The Local Fractional Bootstrap

Publikation: Working paperForskning

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  • rp16_15

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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.
OriginalsprogEngelsk
UdgivelsesstedAarhus
UdgiverInstitut for Økonomi, Århus Universitet
Antal sider32
StatusUdgivet - 6 maj 2016
SerietitelCREATES Research Papers
Nummer2016-15

    Forskningsområder

  • Brownian semistationary process; roughness; fractal index; Hölder regularity; fractional Brownian motion; bootstrap; stochastic volatility; turbulence

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