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

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Author Info
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)

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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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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
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Handle: RePEc:nuf:econwp:0428

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

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  1. 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.
  2. 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. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
  4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  5. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  6. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society. [Downloadable!]
  7. 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. [Downloadable!] (restricted)
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  8. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 525-554. [Downloadable!] (restricted)
  9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March. [Downloadable!] (restricted)
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  10. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Power Variation and Time Change," Economics Papers 2002-W24, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  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. [Downloadable!] (restricted)
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  12. 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. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
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  1. Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," OFRC Working Papers Series 2005fe09, Oxford Financial Research Centre. [Downloadable!]
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  2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2005. "Roughing it Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," NBER Working Papers 11775, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Michiel de Pooter & Martin Martens & Dick van Dijk, 2005. "Predicting the Daily Covariance Matrix for S&P 100 Stocks Using Intraday Data - But Which Frequency to Use?," Tinbergen Institute Discussion Papers 05-089/4, Tinbergen Institute, revised 03 Jan 2006. [Downloadable!]
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  4. Yacine Ait-Sahalia & Per A. Mykland & Lan Zhang, 2005. "Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise," NBER Working Papers 11380, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Klaus Keller & Gary Yohe & Michael Schlesinger, 2005. "Managing the Risks of Climate Thresholds: Uncertainties and Information Needs," Wesleyan Economics Working Papers 2005-009, Wesleyan University, Department of Economics. [Downloadable!]
  6. Jeremy Large, 2005. "Estimating quadratic variation when quoted prices jump by a constant increment," OFRC Working Papers Series 2005fe05, Oxford Financial Research Centre. [Downloadable!]
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  7. Ole E. Barndorff-Nielsen & Neil Shephard & Matthias Winkel, 2005. "Limit theorems for multipower variation in the presence of jumps," Economics Papers 2005-W07, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  8. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2005. "Edgeworth Expansions for Realized Volatility and Related Estimators," NBER Technical Working Papers 0319, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  9. Ole Barndorff-Nielsen & Neil Shephard, 2004. "Multipower Variation and Stochastic Volatility," Economics Papers 2004-W30, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  10. 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. [Downloadable!]
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  11. B. Jungbacker & S.J. Koopman, 2005. "Model-based Measurement of Actual Volatility in High-Frequency Data," Tinbergen Institute Discussion Papers 05-002/4, Tinbergen Institute. [Downloadable!]
  12. Torben G. Andersen & Luca Benzoni, 2007. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," CREATES Research Papers 2007-25, School of Economics and Management, University of Aarhus. [Downloadable!]
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  13. Peter C. B. Phillips & Jun Yu, 2005. "Comments on “A Selective Overview of Nonparametric Methods in Financial Econometrics” by Jianqing Fan," Working Papers 08-2005, Singapore Management University, School of Economics. [Downloadable!]
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