Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data

50 Pages Posted: 7 Oct 2009 Last revised: 26 May 2010

See all articles by Kim Christensen

Kim Christensen

Aarhus University - CREATES

Silja Kinnebrock

University of Oxford

Mark Podolskij

Aarhus University - School of Economics and Management

Date Written: April 2010

Abstract

We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be configured to possess an optimal convergence rate or to ensure positive semi-definite covariance matrix estimates. We also derive a noise-robust Hayashi-Yoshida estimator that can be implemented on the original data without prior alignment of prices. We uncover the finite sample properties of our estimators with simulations and illustrate their practical use on high-frequency equity data.

Keywords: Central limit theorem, Diffusion models, High-frequency data, Market microstructure noise, Non-synchronous trading, Pre-averaging, Realised covariance

JEL Classification: C10, C22, C80

Suggested Citation

Christensen, Kim and Kinnebrock, Silja and Podolskij, Mark, Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data (April 2010). Journal of Econometrics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1483840

Kim Christensen (Contact Author)

Aarhus University - CREATES ( email )

Department of Economics and Business Economics
Fuglesangs Allé 4
Aarhus V, 8210
Denmark

Silja Kinnebrock

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

Mark Podolskij

Aarhus University - School of Economics and Management ( email )

Building 350
DK-8000 Aarhus C
Denmark

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