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

  • OLE E. BARNDORFF-NIELSEN
  • PETER REINHARD HANSEN
  • ASGER LUNDE
  • NEIL SHEPHARD

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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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2004fe20.

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Date of creation: 2004
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Handle: RePEc:sbs:wpsefe:2004fe20
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  1. Roel C. A. Oomen, 2005. "Properties of Bias-Corrected Realized Variance Under Alternative Sampling Schemes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 555-577.
  2. repec:ltr:wpaper:1999.01 is not listed on IDEAS
  3. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society.
  4. 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.
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  8. 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.
  9. Bollen, Bernard & Inder, Brett, 2002. "Estimating daily volatility in financial markets utilizing intraday data," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 551-562, December.
  10. 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.
  11. Yacine Ait-Sahalia & Per A. Mykland, 2003. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," NBER Working Papers 9611, National Bureau of Economic Research, Inc.
  12. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  13. 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.
  14. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  15. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Power Variation and Time Change," Economics Papers 2002-W24, Economics Group, Nuffield College, University of Oxford.
  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. 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.
  18. 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.
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