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An Econometric Analysis of Modulated Realised Covariance, Regression and Correlation in Noisy Diffusion Models

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Author Info
Silja Kinnebrock
Mark Podolskij () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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Abstract

This paper introduces a new estimator to measure the ex-post covariation between high-frequency financial time series under market microstructure noise. We provide an asymptotic limit theory (including feasible central limit theorems) for standard methods such as regression, correlation analysis and covariance, for which we obtain the optimal rate of convergence. We demonstrate some positive semidefinite estimators of the covariation and construct a positive semidefinite estimator of the conditional covariance matrix in the central limit theorem. Furthermore, we indicate how the assumptions on the noise process can be relaxed and how our method can be applied to non-synchronous observations. We also present an empirical study of how high-frequency correlations, regressions and covariances change through time.

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Publisher Info
Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-23.

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Length: 48
Date of creation: 16 May 2008
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Handle: RePEc:aah:create:2008-23

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Web page: http://www.econ.au.dk/afn/

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Related research
Keywords: Central Limit Theorem; Diffusion Models; Market Microstructure Noise; Non-synchronous Trading; High-Frequency Data; Semimartingale Theory;

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This paper has been announced in the following NEP Reports: 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. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Papers 2006-W03, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  2. 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. [Downloadable!]
  3. Michael W. Brandt & Francis X. Diebold, 2006. "A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," Journal of Business, University of Chicago Press, vol. 79(1), pages 61-74, January. [Downloadable!]
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  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Econometric Analysis of Realised Covariation: High Frequency Covariance, Regression and Correlation in Financial Economics," Economics Papers 2002-W13, Economics Group, Nuffield College, University of Oxford, revised 18 Mar 2002. [Downloadable!]
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  5. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," OFRC Working Papers Series 2008fe29, Oxford Financial Research Centre. [Downloadable!]
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  6. Ole BARNDORFF-NIELSEN & Svend Erik GRAVERSEN & Jean JACOD & Mark PODOLSKIJ & Neil SHEPHARD, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," OFRC Working Papers Series 2004fe21, Oxford Financial Research Centre. [Downloadable!]
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  7. 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. [Downloadable!]
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  8. Jean Jacod & Yingying Li & Per A. Mykland & Mark Podolskij & Mathias Vetter, 2007. "Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9," CREATES Research Papers 2007-43, School of Economics and Management, University of Aarhus. [Downloadable!]
  9. 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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  10. 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)
  11. 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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(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. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Economics Papers 2008-W10, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
    Other versions:
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