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Power variation for Gaussian processes with stationary increments

  • Ole E. Barndorff-Nielsen
  • José Manuel Corcuera
  • Mark Podolskij

    ()

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-42.

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Length: 24
Date of creation: 07 Dec 2007
Date of revision:
Handle: RePEc:aah:create:2007-42
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Neil Shephard & Matthias Winkel & Ole E. Barndorff-Nielsen, 2005. "Limit theorems for multipower variation in the presence of jumps," Economics Series Working Papers 2005-FE-06, University of Oxford, Department of Economics.
  2. Ole BARNDORFF-NIELSEN & Svend Erik GRAVERSEN & Jean JACOD & Mark PODOLSKIJ & Neil SHEPHARD, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," OFRC Working Papers Series 2004fe21, Oxford Financial Research Centre.
  3. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Economics Series Working Papers 2003-W12, University of Oxford, Department of Economics.
  4. 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.
  5. Woerner Jeannette H. C., 2003. "Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 47-68, January.
  6. León, José & Ludeña, Carenne, 2007. "Limits for weighted p-variations and likewise functionals of fractional diffusions with drift," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 271-296, March.
  7. Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Papers 2005-W06, Economics Group, Nuffield College, University of Oxford.
  8. Gabriel Lang & François Roueff, 2001. "Semi-parametric Estimation of the Hölder Exponent of a Stationary Gaussian Process with Minimax Rates," Statistical Inference for Stochastic Processes, Springer, vol. 4(3), pages 283-306, October.
  9. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2007. "Power variation for Gaussian processes with stationary increments," CREATES Research Papers 2007-42, School of Economics and Management, University of Aarhus.
  10. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
  11. Kinnebrock, Silja & Podolskij, Mark, 2008. "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1056-1070, June.
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