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Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading

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Author Info
Ole E. Barndorff-Nielsen ()
Peter Reinhard Hansen ()
Asger Lunde ()
Neil Shephard ()

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Abstract

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement noise of certain types and can also handle non-synchronous trading. It is the first estimator which has these three properties which are all essential for empirical work in this area. We derive the large sample asymptotics of this estimator and assess its accuracy using a Monte Carlo study. We implement the estimator on some US equity data, comparing our results to previous work which has used returns measured over 5 or 10 minutes intervals. We show the new estimator is substantially more precise.

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2008fe29.

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Length: 41
Date of creation: 2008
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Handle: RePEc:sbs:wpsefe:2008fe29

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Web page: http://www.finance.ox.ac.uk
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Related research
Keywords: HAC estimator; Long run variance estimator; Market frictions; Quadratic variation; Realised variance;

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Find related papers by JEL classification:
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. deB. Harris, Frederick H. & McInish, Thomas H. & Shoesmith, Gary L. & Wood, Robert A., 1995. "Cointegration, Error Correction, and Price Discovery on Informationally Linked Security Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(04), pages 563-579, December. [Downloadable!]
  2. Silja Kinnebrock & Mark Podolskij, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," OFRC Working Papers Series 2007fe03, Oxford Financial Research Centre. [Downloadable!]
  3. Tim Bollerslev & Hao Zhou, 2007. "Expected Stock Returns and Variance Risk Premia," CREATES Research Papers 2007-17, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  4. Ilze Kalnina & Oliver Linton, 2006. "Estimating Quadratic VariationConsistently in thePresence of Correlated MeasurementError," STICERD - Econometrics Paper Series /2006/509, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  5. Silja Kinnebrock & Mark Podolskij, 2008. "An Econometric Analysis of Modulated Realised Covariance, Regression and Correlation in Noisy Diffusion Models," OFRC Working Papers Series 2008fe25, Oxford Financial Research Centre. [Downloadable!]
    Other versions:
  6. 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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  7. 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)
  8. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129. [Downloadable!] (restricted)
  9. Valeri Voev & Asger Lunde, 2007. "Integrated Covariance Estimation using High-frequency Data in the Presence of Noise," Journal of Financial Econometrics, Oxford University Press, vol. 5(1), pages 68-104. [Downloadable!] (restricted)
  10. 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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  11. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  12. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27. [Downloadable!] (restricted)
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  13. Neil Shephard & Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 264, University of Oxford, Department of Economics. [Downloadable!]
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  14. 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)
  15. Brownlees, C.T. & Gallo, G.M., 2006. "Financial econometric analysis at ultra-high frequency: Data handling concerns," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2232-2245, December. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Silja Kinnebrock & Mark Podolskij, 2008. "An Econometric Analysis of Modulated Realised Covariance, Regression and Correlation in Noisy Diffusion Models," OFRC Working Papers Series 2008fe25, Oxford Financial Research Centre. [Downloadable!]
    Other versions:
  2. Francis X. Diebold & Georg H. Strasser, 2008. "On the Correlation Structure of Microstructure Noise in Theory and Practice," Boston College Working Papers in Economics 692, Boston College Department of Economics. [Downloadable!]
    Other versions:
  3. Ole E. Barndorff-Nielsen & Neil Shephard, 2008. "Modelling and measuring volatility," OFRC Working Papers Series 2008fe31, Oxford Financial Research Centre. [Downloadable!]
  4. Tsiaras, Leonidas, 2009. "The Forecast Performance of Competing Implied Volatility Measures: The Case of Individual Stocks," Finance Research Group Working Papers F-2009-02, University of Aarhus, Aarhus School of Business, Department of Business Studies. [Downloadable!]
  5. Ingmar Nolte & Valeri Voev, 2009. "Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise," CREATES Research Papers 2009-16, School of Economics and Management, University of Aarhus. [Downloadable!]
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