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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

  • Silja Kinnebrock

    (AOPP - Department of Atmospheric, Oceanic and Planetary Physics [Oxford] - University of Oxford)

  • Mark Podolskij

Abstract

We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be configured to possess an optimal convergence rate or to ensure positive semi-definite covariance matrix estimates. We also derive a noise-robust Hayashi-Yoshida estimator that can be implemented on the original data without prior alignment of prices. We uncover the finite sample properties of our estimators with simulations and illustrate their practical use on high-frequency equity data.

Suggested Citation

  • Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Post-Print hal-00732537, HAL.
    • Handle: RePEc:hal:journl:hal-00732537
    DOI: 10.1016/j.jeconom.2010.05.001
    Note: View the original document on HAL open archive server: https://hal.science/hal-00732537
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    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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