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

作者：Corcuera Jose Manuel; Hedevang Emil; Pakkanen Mikko S; Podolskij Mark^*

来源：Stochastic Processes and Their Applications, 2013, 123(7): 2552-2574.

DOI：10.1016/j.spa.2013.03.011

• Brownian semi-stationary processes
• High frequency data
• Limit theorems
• Stable convergence
• Turbulence

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.

• 出版日期2013-7