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Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data

  • Kim Christensen

    ()

    (Aarhus University and CREATES)

  • Silja Kinnebrock

    ()

    (Oxford-Man Institute of Quantitative Finance, Oxford University)

  • Mark Podolskij

    ()

    (ETH Zürich, Switzerland and CREATES, Aarhus University)

In this paper, we show how simple pre-averaging can be applied to measure the ex-post covariance of high-frequency financial time series under market microstructure noise and non-synchronous trading. A modulated realised covariance based on pre-averaged data is proposed and studied in this setting, and we provide complete large sample asymptotics for this new estimator, including feasible central limit theorems for standard methods such as covariance, regression, and correlation analysis. We discuss several versions of the modulated realised covariance, which can be designed to possess an optimal rate of convergence or to guarantee positive semi-definite covariance matrix estimates. We also derive a pre-averaged version of the Hayashi-Yoshida estimator that can be applied directly to the noisy and nonsynchronous data without any prior alignment of prices. An empirical study illustrates how high-frequency covariances, regression coefficients, and correlations change through time.

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Paper provided by Department of Economics and Business Economics, Aarhus University in its series CREATES Research Papers with number 2009-45.

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Length: 34
Date of creation: 01 Sep 2009
Date of revision:
Handle: RePEc:aah:create:2009-45
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  11. 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, Department of Economics and Business Economics, Aarhus University.
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  16. Vetter, Mathias & Podolskij, Mark, 2006. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," Technical Reports 2006,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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