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

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  • 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.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 397.

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Date of creation: 01 Jul 2008
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Handle: RePEc:oxf:wpaper:397

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Keywords: HAC Estimator; Long Run Variance Estimator; Market Frictions; Quadratic Variation; Realised Variance;

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