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

José Manuel Corcuera, Emil Hedevang, Mikko S. Pakkanen and Mark Podolskij

Stochastic Processes and their Applications, 2013, vol. 123, issue 7, 2552-2574

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 by Barndorff-Nielsen et al. (2011) [4] and Barndorff-Nielsen (2012) [5] 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)
Date: 2013
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Citations: View citations in EconPapers (21)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:7:p:2552-2574

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DOI: 10.1016/j.spa.2013.03.011

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