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The Local Fractional Bootstrap | | Mikkel Bennedsen
; Ulrich Hounyo
; Asger Lunde
; Mikko S. Pakkanen
; | | Date: |
3 May 2016 | | 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. | | Source: | arXiv, 1605.0868 | | Services: | Forum | Review | PDF | Favorites | |
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