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A Note on the Central Limit Theorem for Bipower Variation of General Functions

Author

Listed:
  • Silja Kinnebrock
  • Mark Podolskij
  • Ruhr-Universitat Bochum

Abstract

In this paper we present the central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in Barndorff-Nielsen, Graversen, Jacod, Podolskij and Shephard (2006), who showed the central limit theorem for even functions. We prove an infeasible central limit theorem for general functions and state some assumptions under which a feasible version of our results can be obtained. Finally, we present some examples from the literature to which our theory can be applied.

Suggested Citation

  • Silja Kinnebrock & Mark Podolskij & Ruhr-Universitat Bochum, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," Economics Series Working Papers 2007-FE-03, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:2007-fe-03
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    Citations

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    Cited by:

    1. Ole E. Barndorff-Nielsen & Silja Kinnebrock & Neil Shephard, 2008. "Measuring downside risk - realised semivariance," OFRC Working Papers Series 2008fe01, Oxford Financial Research Centre.
    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. Neil Shephard & Silja Kinnebrock & Ole E. Barndorff-Neilsen, 2008. "Measuring downside risk - realised semivariance," Economics Series Working Papers 382, University of Oxford, Department of Economics.

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