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Asymptotic theory for Brownian semi-stationary processes with application to turbulence

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Author Info

  • José Manuel Corcuera

    ()
    (Universitat de Barcelona)

  • Emil Hedevang

    ()
    (Aarhus University)

  • Mikko S. Pakkanen

    ()
    (Aarhus University and CREATES)

  • Mark Podolskij

    ()
    (Heidelberg University and CREATES)

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    Abstract

    This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in [Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2011): Multipower variation for Brownian semistationary processes. Bernoulli 17(4), 1159-1194; Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2012): Limit theorems for functionals of higher order differences of Brownian semi-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data.

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    Bibliographic Info

    Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-52.

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    Length: 25
    Date of creation: 16 Nov 2012
    Date of revision:
    Handle: RePEc:aah:create:2012-52

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    Web page: http://www.econ.au.dk/afn/

    Related research

    Keywords: Brownian semi-stationary processes; high frequency data; limit theorems; stable convergence; turbulence;

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    References

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    1. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    2. Gabriel Lang & François Roueff, 2001. "Semi-parametric Estimation of the Hölder Exponent of a Stationary Gaussian Process with Minimax Rates," Statistical Inference for Stochastic Processes, Springer, vol. 4(3), pages 283-306, October.
    3. Mark Podolskij & Mathias Vetter, 2009. "Understanding limit theorems for semimartingales: a short survey," CREATES Research Papers 2009-47, School of Economics and Management, University of Aarhus.
    4. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, School of Economics and Management, University of Aarhus.
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    Cited by:
    1. Mikko S. Pakkanen, 2013. "Limit theorems for power variations of ambit fields driven by white noise," CREATES Research Papers 2013-01, School of Economics and Management, University of Aarhus.

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