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Bipower variation for Gaussian processes with stationary increments

  • Ole E. Barndorff-Nielsen
  • José Manuel Corcuera
  • Mark Podolskij
  • Jeannette H.C. Woerner

    ()

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

Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing limit laws, due to Nualart, Peccati and others.

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File URL: ftp://ftp.econ.au.dk/creates/rp/08/rp08_21.pdf
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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-21.

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Length: 27
Date of creation: 08 May 2008
Date of revision:
Handle: RePEc:aah:create:2008-21
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Economics Papers 2003-W12, Economics Group, Nuffield College, University of Oxford.
  2. Barndorff-Nielsen, Ole E. & Corcuera, José Manuel & Podolskij, Mark, 2009. "Power variation for Gaussian processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1845-1865, June.
  3. 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.
  4. Barndorff-Nielsen, Ole E. & Shephard, Neil & Winkel, Matthias, 2006. "Limit theorems for multipower variation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 796-806, May.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Series Working Papers 2005-FE-09, University of Oxford, Department of Economics.
  10. 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.
  11. 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.
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