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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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| Authors: | Ole E Barndorff-Nielsen Peter Reinhard Hansen Asger Lunde Neil Shephard |
| Institution: | a The T.N. Thiele Centre for Mathematics in Natural Science, Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark;b CREATES, University of Aarhus, Denmark;c Department of Economics, Stanford University, Landau Economics Building, 579 Serra Mall, Stanford, CA 94305-6072, USA;d School of Economics and Management, Aarhus University, Bartholins Allé 10, DK-8000 Aarhus C, Denmark;e Oxford-Man Institute, University of Oxford, Eagle House, Walton Well Road, Oxford OX2 6ED, UK;f Department of Economics, University of Oxford, UK |
| 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 error 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 min intervals. We show that the new estimator is substantially more precise. |
| Keywords: | HAC estimator Long run variance estimator Market frictions Quadratic variation Realised variance |
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