Power variation for Gaussian processes with stationary increments

Ole Barndorff-Nielsen, José Manuel Corcuera and Mark Podolskij (mpodolskij@creates.au.dk)

Stochastic Processes and their Applications, 2009, vol. 119, issue 6, 1845-1865

Abstract: We develop the asymptotic theory for the realised power variation of the processes X=[phi]-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 conditions on the path of the process [phi] we prove the convergence in probability for the properly normalised realised power variation. Moreover, under a further assumption on the Hölder index of the path of [phi], we show an associated stable central limit theorem. The main tool is a general central limit theorem, due essentially to Hu and Nualart [Y. Hu, D. Nualart, Renormalized self-intersection local time for fractional Brownian motion, Ann. Probab. (33) (2005) 948-983], Nualart and Peccati [D. Nualart, G. Peccati, Central limit theorems for sequences of multiple stochastic integrals, Ann. Probab. (33) (2005) 177-193] and Peccati and Tudor [G. Peccati, C.A. Tudor, Gaussian limits for vector-valued multiple stochastic integrals, in: M. Emery, M. Ledoux, M. Yor (Eds.), Seminaire de Probabilites XXXVIII, in: Lecture Notes in Math, vol. 1857, Springer-Verlag, Berlin, 2005, pp. 247-262], for sequences of random variables which admit a chaos representation.

Keywords: Central; limit; theorem; Chaos; expansion; Gaussian; processes; High-frequency; data; Multiple; Wiener-Ito; integrals; Power; variation (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (28)

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Related works:
Working Paper: Bipower variation for Gaussian processes with stationary increments (2008)
Working Paper: Power variation for Gaussian processes with stationary increments (2007)
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