Power variation for Gaussian processes with stationary increments

Ole Barndorff-Nielsen, José Manuel Corcuera and Mark Podolskij ()

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

Abstract: We develop the asymptotic theory for the realised power variation of the processes X = f • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of the process f we prove the convergence in probability for the properly normalised realised power variation. Moreover, under a further assumption on the H¨older index of the path of f, we show an associated stable central limit theorem. The main tool is a general central limit theorem, due essentially to Hu & Nualart (2005), Nualart & Peccati (2005) and Peccati & Tudor (2005), for sequences of random variables which admit a chaos representation.

Keywords: Central Limit Theorem; Chaos Expansion; Gaussian Processes; High-Frequency Data; Multiple Wiener-Itô Integrals; Power Variation (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
Pages: 24
Date: 2007-12-07
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mst
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Power variation for Gaussian processes with stationary increments (2009)
Working Paper: Bipower variation for Gaussian processes with stationary increments (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2007-42

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