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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


University of Aarhus - Thiele Centre, Department of Mathematical Sciences

Peter Reinhard Hansen


European University Institute - Economics Department (ECO); University of Aarhus - CREATES

Asger Lunde


University of Aarhus - School of Economics and Management; CREATES

Neil Shephard


University 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 series


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Date posted: July 2, 2008 ; Last revised: July 14, 2010

Suggested Citation

Barndorff-Nielsen, Ole E., Hansen, Peter Reinhard, Lunde, Asger and Shephard, Neil, Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading (July 14, 2010). Available at SSRN: http://ssrn.com/abstract=1154144 or http://dx.doi.org/10.2139/ssrn.1154144

Contact Information

Ole E. Barndorff-Nielsen
University of Aarhus - Thiele Centre, Department of Mathematical Sciences ( email )
Ny Munkegade
Aarhus, DK 8000
Denmark
Peter Reinhard Hansen (Contact Author)
European University Institute - Economics Department (ECO) ( email )
Villa San Paolo
Via della Piazzuola 43
50133 Florence
Italy
University of Aarhus - CREATES ( email )
School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark
Asger Lunde
University of Aarhus - School of Economics and Management ( email )
Aarhus
Denmark
CREATES ( email )
School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark
Neil Shephard
University of Oxford - Oxford-Man Institute ( email )
Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom
44 1865 616600 (Phone)
44 1865 616601 (Fax)
HOME PAGE: http://www.oxford-man.ox.ac.uk
University of Oxford - Nuffield College ( email )
New Road
Oxford, OX1 1NF
United Kingdom
44 1865 278593 (Phone)
44 1865 278500 (Fax)
University of Oxford - Oxford Financial Research Centre ( email )
Oxford
United Kingdom
HOME PAGE: http://www.finance.ox.ac.uk
Feedback to SSRN (Beta)


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