Limit theorems for functionals of higher order differences of Brownian semi-stationary processes

Ole Barndorff-Nielsen, José Manuel Corcuera () and Mark Podolskij ()
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José Manuel Corcuera: University of Barcelona, Postal: Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain

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

Abstract: We present some new asymptotic results for functionals of higher order differences of Brownian semi-stationary processes. In an earlier work [4] we have derived a similar asymptotic theory for first order differences. However, the central limit theorems were valid only for certain values of the smoothness parameter of a Brownian semistationary process, and the parameter values which appear in typical applications, e.g. in modeling turbulent flows in physics, were excluded. The main goal of the current paper is the derivation of the asymptotic theory for the whole range of the smoothness parameter by means of using second order differences. We present the law of large numbers for the multipower variation of the second order differences of Brownian semi-stationary processes and show the associated central limit theorem. Finally, we demonstrate some estimation methods for the smoothness parameter of a Brownian semi-stationary process as an application of our probabilistic results.

Keywords: Brownian semi-stationary processes; central limit theorem; Gaussian processes; high frequency observations; higher order differences; multipower variation; stable convergence. (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
Pages: 26
Date: 2009-12-21
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (1)

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