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Limit theorems for multipower variation in the presence of jumps

Author

Listed:
  • Ole E. Barndorff-Nielsen

    () (Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark)

  • Neil Shephard

    () (Nuffield College, Oxford)

  • Matthias Winkel

    () (Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, U.K.)

Abstract

In this paper we provide a systematic study of the robustness of probability limits and central limit theory for realised multipower variation when we add finite activity and infinite activity jump processes to an underlying Brownian semimartingale.

Suggested Citation

  • 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.
  • Handle: RePEc:nuf:econwp:0507
    as

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    File URL: http://www.nuffield.ox.ac.uk/economics/papers/2005/w7/winkel06.pdf
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    References listed on IDEAS

    as
    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    3. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    4. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
    5. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
    6. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Econometric Analysis of Realised Covariation: High Frequency Covariance, Regression and Correlation in Financial Economics," Economics Papers 2002-W13, Economics Group, Nuffield College, University of Oxford, revised 18 Mar 2002.
    7. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    8. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," OFRC Working Papers Series 2004fe20, Oxford Financial Research Centre.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Bipower variation; Infinite activity; Multipower variation; Power variation; Quadratic variation; Semimartingales; Stochastic volatility;

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