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Limit theorems for multipower variation in the presence of jumps

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  • Barndorff-Nielsen, Ole E.
  • Shephard, Neil
  • Winkel, Matthias

Abstract

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

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 116 (2006)
Issue (Month): 5 (May)
Pages: 796-806

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Handle: RePEc:eee:spapps:v:116:y:2006:i:5:p:796-806

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Related research

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

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References

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  1. 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.
  2. 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," Economics Papers 2004-W28, Economics Group, Nuffield College, University of Oxford.
  3. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics," Economics Series Working Papers 2002-FE-03, University of Oxford, Department of Economics.
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford.
  5. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometrics of testing for jumps in financial economics using bipower variation ," OFRC Working Papers Series 2004fe01, Oxford Financial Research Centre.
  6. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  7. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
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