Multipower Variation for Brownian Semistationary Processes

CREATES Research Paper No. 2009-21

47 Pages Posted: 28 May 2009

See all articles by Ole E. Barndorff-Nielsen

Ole E. Barndorff-Nielsen

University of Aarhus - Thiele Centre, Department of Mathematical Sciences

José Manuel Corcuera

University of Barcelona - Faculty of Mathematics

Mark Podolskij

Aarhus University - School of Business and Social Sciences

Date Written: May 28, 2009

Abstract

In this paper we study the asymptotic behaviour of power and multipower variations of stochatstic processes. Processes of the type considered serve in particular, to analyse data of velocity increments of a uid in a turbulence regime with spot intermittency sigma. The purpose of the present paper is to determine the probabilistic limit behaviour of the (multi)power variations of Y, as a basis for studying properties of the intermittency process. Notably the processes Y are in general not of the semimartingale kind and the established theory of multipower variation for semimartingales does not suffice for deriving the limit properties. As a key tool for the results a general central limit theorem for triangular Gaussian schemes is formulated and proved. Examples and an application to realised variance ratio are given.

Keywords: Central Limit Theorem, Gaussian Processes, Intermittency, Nonsemimartingales, Turbulence, Volatility, Wiener Chaos

JEL Classification: C10, C80

Suggested Citation

Barndorff-Nielsen, Ole E. and Corcuera Valverde, José Manuel and Podolskij, Mark, Multipower Variation for Brownian Semistationary Processes (May 28, 2009). CREATES Research Paper No. 2009-21, Available at SSRN: https://ssrn.com/abstract=1411030 or http://dx.doi.org/10.2139/ssrn.1411030

Ole E. Barndorff-Nielsen (Contact Author)

University of Aarhus - Thiele Centre, Department of Mathematical Sciences ( email )

Ny Munkegade
Aarhus, DK 8000
Denmark

José Manuel Corcuera Valverde

University of Barcelona - Faculty of Mathematics ( email )

Gran Via de les Corts
Catalanes 585
Barcelona 08007
Spain

Mark Podolskij

Aarhus University - School of Business and Social Sciences ( email )

Building 350
DK-8000 Aarhus C
Denmark

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