The Annals of Statistics

Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency

Markus Bibinger, Nikolaus Hautsch, Peter Malec, and Markus Reiß

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An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semi-parametric efficiency is established in the Cramér–Rao sense. Main findings are that nonsynchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour.

Article information

Ann. Statist., Volume 42, Number 4 (2014), 1312-1346.

First available in Project Euclid: 25 June 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G05: Estimation

Asymptotic equivalence asynchronous observations integrated covolatility matrix high-frequency data semi-parametric efficiency microstructure noise


Bibinger, Markus; Hautsch, Nikolaus; Malec, Peter; Reiß, Markus. Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency. Ann. Statist. 42 (2014), no. 4, 1312--1346. doi:10.1214/14-AOS1224.

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