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Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise

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  • Ole E. Barndorff-Nielsen

    (University of Aarhus)

  • Peter Reinhard Hansen

    (Stanford University)

  • Asger Lunde

    (Aarhus School of Business)

  • Neil Shephard

    ()
    (Nuffield College, University of Oxford)

Abstract

We consider kernel-based estimators of integrated variances in the presence of independent market microstructure effects. We derive the bias and variance properties for all regular kernel-based estimators and derive a lower bound for their asymptotic variance. Further we show that the subsample-based estimator is closely related to a Bartlett-type kernel estimator. The small difference between the two estimators due to end effects, turns out to be key for the consistency of the subsampling estimator. This observation leads us to a modified class of kernel-based estimators, which are also consistent. We study the efficiency of our new kernel-based procedure. We show that optimal modified kernel-based estimator converges to the integrated variance at the optimal rate, m^1/4, where m is the number of intraday returns.

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File URL: http://www.nuff.ox.ac.uk/economics/papers/2004/w28/RVkernel10.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2004-W28.

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Length: 42 pages
Date of creation: 15 Nov 2004
Date of revision:
Handle: RePEc:nuf:econwp:0428

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Web page: http://www.nuff.ox.ac.uk/economics/

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  1. Shephard, Neil, 1993. "Distribution of the ML Estimator of an MA(1) and a local level model," Econometric Theory, Cambridge University Press, vol. 9(03), pages 377-401, June.
  2. Roel Oomen, 2004. "Properties of Bias Corrected Realized Variance Under Alternative Sampling Schemes," Working Papers wp04-15, Warwick Business School, Finance Group.
  3. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  4. Tanaka, Katsuto & Satchell, S.E., 1989. "Asymptotic Properties of the Maximum-Likelihood and Nonlinear Least-Squares Estimators for Noninvertible Moving Average Models," Econometric Theory, Cambridge University Press, vol. 5(03), pages 333-353, December.
  5. 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.
  6. Bernard Bollen & Brett Inder, 1999. "Estimating Daily Volatility in Financial Markets Utilizing Intraday Data," Working Papers 1999.01, School of Economics, La Trobe University.
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  8. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
  9. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  10. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  11. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Power Variation and Time Change," Economics Papers 2002-W24, Economics Group, Nuffield College, University of Oxford.
  12. 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.
  13. 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.
  14. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  15. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 525-554.
  16. 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.
  17. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society.
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