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

José Manuel Corcuera (), Emil Hedevang (), Mikko S. Pakkanen () and Mark Podolskij ()
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José Manuel Corcuera: Universitat de Barcelona, Postal: Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
Emil Hedevang: Aarhus University, Postal: Department of Mathematics, Ny Munkegade 118, 8000 Aarhus C, Denmark
Mikko S. Pakkanen: Aarhus University and CREATES, Postal: Department of Economics and Business, Fuglesangs Alle 4, 8210 Aarhus V, Denmark
Mark Podolskij: Heidelberg University and CREATES, Postal: Department of Mathematics, 69120 Heidelberg, Germany

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

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.

Keywords: Brownian semi-stationary processes; high frequency data; limit theorems; stable convergence; turbulence (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
Pages: 25
Date: 2012-11-16
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mst
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Citations: View citations in EconPapers (1)

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