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Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous TradingOle E. Barndorff-NielsenUniversity of Aarhus - Thiele Centre, Department of Mathematical Sciences Peter Reinhard HansenEuropean University Institute - Economics Department (ECO); University of Aarhus - CREATES Asger LundeUniversity of Aarhus - School of Economics and Management; CREATES Neil ShephardUniversity of Oxford - Oxford-Man Institute; University of Oxford - Nuffield College; University of Oxford - Oxford Financial Research Centre July 14, 2010 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.
Number of Pages in PDF File: 53 Keywords: HAC estimator, Long run variance estimator, Market frictions, Quadratic variation, Realised Variance JEL Classification: C13, C32 working papers seriesDate posted: July 2, 2008 ; Last revised: July 14, 2010Suggested CitationContact Information
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