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Limit theorems for bipower variation in financial econometrics

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

Abstract

In this paper we provide an asymptotic analysis of generalised bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation and bipower variations which 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.

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Bibliographic Info

Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2005fe09.

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Date of creation: 2005
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Handle: RePEc:sbs:wpsefe:2005fe09

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  1. 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.
  2. 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.
  3. 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.
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  8. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Realised power variation and stochastic volatility models," Economics Series Working Papers 2001-W18, University of Oxford, Department of Economics.
  9. 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.
  10. Martens, M.P.E. & van Dijk, D.J.C., 2006. "Measuring volatility with the realized range," Econometric Institute Research Papers EI 2006-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  11. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  12. 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.
  13. 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).
  14. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," NBER Working Papers 10914, National Bureau of Economic Research, Inc.
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  16. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, September.
  17. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Series Working Papers 2003-W18, University of Oxford, Department of Economics.
  18. 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.
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  20. Officer, R R, 1973. "The Variability of the Market Factor of the New York Stock Exchange," The Journal of Business, University of Chicago Press, vol. 46(3), pages 434-53, July.
  21. 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.
  22. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  23. G. William Schwert, 1998. "Stock Market Volatility: Ten Years After the Crash," NBER Working Papers 6381, National Bureau of Economic Research, Inc.
  24. Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
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  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.
  27. Neil Shephard & Ole E. Barndorff-Nielsen, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," Economics Series Working Papers 240, University of Oxford, Department of Economics.
  28. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
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