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

  • Ole E. Barndorff-Nielsen


    (Department of Mathematical Sciences, University of Aarhus)

  • Peter Reinhard Hansen


    (Department of Economics, Stanford University)

  • Asger Lunde


    (Aarhus School of Business, University of Aarhus)

  • Neil Shephard


    (Oxford-Man Institute, University of Oxford)

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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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2008-W10.

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Length: 41 pages
Date of creation: 07 Jan 2008
Date of revision:
Handle: RePEc:nuf:econwp:0810
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