On Covariation Estimation for Multivariate Continuous Itô Semimartingales with Noise in Non-Synchronous Observation Schemes

Journal of Multivariate Analysis, Forthcoming

41 Pages Posted: 4 May 2012 Last revised: 14 Jun 2014

See all articles by Kim Christensen

Kim Christensen

Aarhus University - CREATES

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics

Mathias Vetter

Ruhr University of Bochum

Date Written: March 2013

Abstract

This paper presents a Hayashi-Yoshida type estimator for the covariation matrix of continuous Itô semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent nonsynchronous points. The estimator of the covariation matrix is designed via a certain combination of the local averages and the Hayashi-Yoshida estimator. Our method does not require any synchronization of the observation scheme (as e.g. previous tick method or refreshing time method) and it is robust to some dependence structure of the noise process. We show the associated central limit theorem for the proposed estimator and provide a feasible asymptotic result. Our proofs are based on a blocking technique and a stable convergence theorem for semimartingales. Finally, we show simulation results for the proposed estimator to illustrate its finite sample properties.

Keywords: Central limit theorem, Hayashi-Yoshida estimator, high frequency observations, Itô semimartingale, pre-averaging, stable convergence

JEL Classification: C10, C80

Suggested Citation

Christensen, Kim and Podolskij, Mark and Vetter, Mathias, On Covariation Estimation for Multivariate Continuous Itô Semimartingales with Noise in Non-Synchronous Observation Schemes (March 2013). Journal of Multivariate Analysis, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2050642 or http://dx.doi.org/10.2139/ssrn.2050642

Kim Christensen (Contact Author)

Aarhus University - CREATES ( email )

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

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics ( email )

Grabengasse 1
Heidelberg, 69117
Germany
00496221546276 (Phone)

Mathias Vetter

Ruhr University of Bochum ( email )

Universitätsstraße 150
Bochum, NRW 44780
Germany

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