Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise

46 Pages Posted: 18 Nov 2004 Last revised: 6 Apr 2008

See all articles by Ole E. Barndorff-Nielsen

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; Copenhagen Business School, Finance; Aarhus University - CREATES

Asger Lunde

Aarhus University - School of Economics and Management; CREATES

Neil Shephard

Harvard University

Date Written: March 2008

Abstract

This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice.

Keywords: Bipower variation, Long run variance estimator, Market frictions, Quadratic variation, Realized variance, Subsampling

JEL Classification: C13, C22

Suggested Citation

Barndorff-Nielsen, Ole E. and Hansen, Peter Reinhard and Lunde, Asger and Shephard, Neil, Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise (March 2008). Available at SSRN: https://ssrn.com/abstract=620203 or http://dx.doi.org/10.2139/ssrn.620203

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)

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/

Copenhagen Business School, Finance ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

Aarhus University - CREATES ( email )

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

Asger Lunde

Aarhus University - 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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