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

Author

Listed:
  • Neil Shephard
  • Ole E. Barndorff-Nielsen
  • Peter Reinhard Hansen
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.

Suggested Citation

  • Neil Shephard & Ole E. Barndorff-Nielsen & Peter Reinhard Hansen, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Economics Series Working Papers 397, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:397
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    More about this item

    Keywords

    HAC Estimator; Long Run Variance Estimator; Market Frictions; Quadratic Variation; Realised Variance;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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