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Microstructure noise in the continuous case: the pre-averaging approach

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  • Jacod, Jean
  • Li, Yingying
  • Mykland, Per A.
  • Podolskij, Mark
  • Vetter, Mathias

Abstract

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the integrated volatility. We show that our approach, which possess an intuitive transparency, can generate rate optimal estimators (with convergence rate n-1/4). --

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Bibliographic Info

Paper provided by Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen in its series Technical Reports with number 2007,41.

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Date of creation: 2007
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Handle: RePEc:zbw:sfb475:200741

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Keywords: consistency; continuity; discrete observation; Itˆo process; leverage effect; pre-averaging; quarticity; realized volatility; stable convergence;

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  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  2. Yingying Li & Per A. Mykland, 2007. "Are volatility estimators robust with respect to modeling assumptions?," Papers 0709.0440, arXiv.org.
  3. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
  4. Dean P. Foster & Daniel B. Nelson, 1994. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," NBER Technical Working Papers 0163, National Bureau of Economic Research, Inc.
  5. Gallant, A. Ronald & Hsu, Chien-Te & Tauchen, George, 2000. "Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance," Working Papers 00-04, Duke University, Department of Economics.
  6. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  7. Mark Podolskij & Mathias Vetter, 2007. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," CREATES Research Papers 2007-27, School of Economics and Management, University of Aarhus.
  8. Ilze Kalnina & Oliver Linton, 2007. "Inference about Realized Volatility using Infill Subsampling," STICERD - Econometrics Paper Series /2007/523, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  9. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  10. 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.
  11. 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.
  12. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
  13. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
  14. Robert F. Engle, 1996. "The Econometrics of Ultra-High Frequency Data," NBER Working Papers 5816, National Bureau of Economic Research, Inc.
  15. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
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