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Limit Theorems For Bipower Variation In Financial Econometrics

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  • Barndorff-Nielsen, Ole E.
  • Graversen, Svend Erik
  • Jacod, Jean
  • Shephard, Neil

Abstract

In this paper we provide an asymptotic analysis of generalized bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation, and bipower variations that have been highlighted in recent years in financial econometrics. The analysis is carried out under some rather general Brownian semimartingale assumptions, which allow for standard leverage effects.Ole E. Barndorff-Nielsen s work is supported by the Centre for Analytical Finance (CAF), which is funded by the Danish Social Science Research Council. Neil Shephard s research is supported by the UK s ESRC through the grant High frequency financial econometrics based upon power variation. We thank the editor, Peter Phillips, and the referees for their stimulating comments on an earlier version.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 04 (August)
Pages: 677-719

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Handle: RePEc:cup:etheor:v:22:y:2006:i:04:p:677-719_06

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  1. 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.
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  5. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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  8. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  9. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-53, December.
  10. Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," Economics Series Working Papers 2004-FE-20, University of Oxford, Department of Economics.
  11. 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.
  12. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Accuracy of Integrated Volatility Estimators," Working Papers 1225, Queen's University, Department of Economics.
  13. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics," OFRC Working Papers Series 2002fe03, Oxford Financial Research Centre.
  14. Neil Shephard & Ole Barndorff-Nielsen, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Series Working Papers 2004-FE-01, University of Oxford, Department of Economics.
  15. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
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  17. Christensen, Kim & Podolski, Mark, 2005. "Asymptotic theory for range-based estimation of integrated variance of a continuous semi-martingale," Technical Reports 2005,18, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  18. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  19. Ole E. Barndorff-Nielsen & Neil Shephard & Matthias Winkel, 2005. "Limit theorems for multipower variation in the presence of jumps," OFRC Working Papers Series 2005fe06, Oxford Financial Research Centre.
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  22. Andersen, Torben G. & Bollerslev, Tim & Francis X. Diebold,, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," CFS Working Paper Series 2003/35, Center for Financial Studies (CFS).
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  24. G. William Schwert, 1997. "Stock Market Volatility: Ten Years After the Crash," Center for Financial Institutions Working Papers 97-51, Wharton School Center for Financial Institutions, University of Pennsylvania.
  25. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.
  26. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford.
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  29. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
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