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Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading

53 Pages Posted: 2 Jul 2008 Last revised: 14 Jul 2010

Ole E. Barndorff-Nielsen

University of Aarhus - Thiele Centre, Department of Mathematical Sciences

Peter Reinhard Hansen

University of North Carolina (UNC) at Chapel Hill - Department of Economics; University of Aarhus - CREATES

Asger Lunde

University of Aarhus - School of Economics and Management; CREATES

Neil Shephard

Harvard University

Date Written: 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.

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

JEL Classification: C13, C32

Suggested Citation

Barndorff-Nielsen, Ole E. and Hansen, Peter Reinhard and 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: https://ssrn.com/abstract=1154144 or http://dx.doi.org/10.2139/ssrn.1154144

Ole Barndorff-Nielsen

University of Aarhus - Thiele Centre, Department of Mathematical Sciences ( email )

Ny Munkegade
Aarhus, DK 8000
Denmark

Peter Hansen (Contact Author)

University of Aarhus - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Chapel Hill, NC 27599
United States

HOME PAGE: http://https://sites.google.com/site/peterreinhardhansen/

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

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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