The local fractional bootstrap

Mikkel Bennedsen*, Ulrich Hounyo, Asger Lunde, Mikko S. Pakkanen

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


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.

Original languageEnglish
JournalScandinavian Journal of Statistics
Pages (from-to)329-359
Number of pages31
Publication statusPublished - 2019


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


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