Christensen, Kim
[Verfasser:in]
;
Podolskij, Mark
[Sonstige Person, Familie und Körperschaft];
Vetter, Mathias
[Sonstige Person, Familie und Körperschaft]
On Covariation Estimation for Multivariate Continuous Itô Semimartingales with Noise in Non-Synchronous Observation Schemes
Anmerkungen:
In: Journal of Multivariate Analysis, Forthcoming
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments March 2013 erstellt
Beschreibung:
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