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
Date Written: March 2013
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: Suggested Citation