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On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes

Kim Christensen, Mark Podolskij, Mathias Vetter

arXiv 23 Feb 2026 · Econometrics

arXiv:2602.19658 · PDF · Extracted main text

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 non-synchronous 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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Christensen, K., S. Kinnebrock and M. Podolskij (2010) Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data self1.00084100%
2Jacod, J., Y. Li, P. Mykland, M. Podolskij and M. Vetter (2009) Microstructure noise in the continuous case: the pre-averaging approach self1.00064100%
3Bibinger, M (2011) Efficient covariance estimation for asynchronous noisy high-frequency data0.64422100%
4Barndorff-Nielsen, O.E., S.E. Graversen, J. Jacod, M. Podolskij, N.… (2006) A central limit theorem for realised power and bipower variations of continuous semimartingales self0.64422100%
5Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard (2010) Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and n…0.64422100%
6Jacod, J., M. Podolskij and M. Vetter (2010) Limit theorems for moving averages of discretized processes plus noise self0.64422100%
7Jacod, J. and A.N. Shiryaev (2003) Limit Theorems for Stochastic Processes, 2d ed., Springer-Verlag: Berlin0.64422100%
8Podolskij, M. and M. Vetter (2009) Bipower-type estimation in a noisy diffusion setting self0.64422100%
9Podolskij, M. and M. Vetter (2009) Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps self0.64422100%
10Gloter, A. and J. Jacod (2001) Diffusions with measurement errors0.51121100%

Showing the top 10 of 23 scored citations.