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Multipower Variation for Brownian Semistationary Processes

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Author Info

  • Ole E. Barndorff-Nielsen

    () (Aarhus University and CREATES)

  • José Manuel Corcuera

    () (Universitat de Barcelona)

  • Mark Podolskij

    () (ETH Zürich and CREATES)

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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-21.

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Length: 45
Date of creation: 26 May 2009
Date of revision:
Handle: RePEc:aah:create:2009-21

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Web page: http://www.econ.au.dk/afn/

Related research

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

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References

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  1. Ho, Hwai-Chung & Sun, Tze-Chien, 1987. "A central limit theorem for non-instantaneous filters of a stationary Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 144-155, June.
  2. Barndorff-Nielsen, Ole Eiler & Graversen, Svend Erik & Jacod, Jean & Podolskij, Mark, 2004. "A central limit theorem for realised power and bipower variations of continuous semimartingales," Technical Reports 2004,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  3. Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(02), pages 331-368, April.
  4. Ole E. Barndorff-Nielsen & Neil Shephard & Matthias Winkel, 2005. "Limit theorems for multipower variation in the presence of jumps," Economics Papers 2005-W07, Economics Group, Nuffield College, University of Oxford.
  5. Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," OFRC Working Papers Series 2005fe09, Oxford Financial Research Centre.
  6. Barndorff-Nielsen, Ole E. & Shephard, Neil, 2006. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 217-252.
  7. Silja Kinnebrock & Mark Podolskij, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," OFRC Working Papers Series 2007fe03, Oxford Financial Research Centre.
  8. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij & Jeannette H.C. Woerner, 2008. "Bipower variation for Gaussian processes with stationary increments," CREATES Research Papers 2008-21, School of Economics and Management, University of Aarhus.
  9. Nualart, D. & Ortiz-Latorre, S., 2008. "Central limit theorems for multiple stochastic integrals and Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 614-628, April.
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Citations

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Cited by:
  1. José Manuel Corcuera & Emil Hedevang & Mikko S. Pakkanen & Mark Podolskij, 2012. "Asymptotic theory for Brownian semi-stationary processes with application to turbulence," CREATES Research Papers 2012-52, School of Economics and Management, University of Aarhus.
  2. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Limit theorems for functionals of higher order differences of Brownian semi-stationary processes," CREATES Research Papers 2009-60, School of Economics and Management, University of Aarhus.
  3. Nourdin, Ivan & Peccati, Giovanni & Podolskij, Mark, 2011. "Quantitative Breuer-Major theorems," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 793-812, April.
  4. Mark Podolskij & Katrin Wasmuth, 2012. "Goodness-of-fit testing for fractional diffusions," CREATES Research Papers 2012-12, School of Economics and Management, University of Aarhus.

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