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

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2009. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," CREATES Research Papers 2009-45, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2009-45
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Central limit theorem; Diffusionmodels; High-frequency data; Marketmicrostructure noise; Non-synchronous trading; Pre-averaging; Realised covariance;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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