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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
Thiele Centre, Dept. Math. Sciences, Univ. Aarhus

Peter Reinhard Hansen
Stanford University; 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 27, 2008


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.

Keywords: HAC estimator, Long run variance estimator, Market frictions, Quadratic variation, Realised Variance

JEL Classifications: C13, C32

Working Paper Series

Date posted: July 02, 2008 ; Last revised: December 17, 2008

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 27, 2008). Available at SSRN: http://ssrn.com/abstract=1154144


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Contact Information

Peter Reinhard Hansen (Contact Author)
Stanford University ( email )
Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
650-725-1869 (Phone)
650-725-5702 (Fax)
HOME PAGE: http://www.stanford.edu/~prhansen
University of Aarhus - CREATES ( email )
School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C Denmark
Ole E. Barndorff-Nielsen
Thiele Centre, Dept. Math. Sciences, Univ. Aarhus ( email )
Ny Munkegade
Aarhus DK 8000
Denmark
Asger Lunde
University of Aarhus - School of Economics and Management
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 )
Blue Boar Court
9 Alfred Street
Oxford, Oxfordshire OX30DL
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
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References: 64
Citations: 7

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