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August 2014 Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency
Markus Bibinger, Nikolaus Hautsch, Peter Malec, Markus Reiß
Ann. Statist. 42(4): 1312-1346 (August 2014). DOI: 10.1214/14-AOS1224

Abstract

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.

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Markus Bibinger. Nikolaus Hautsch. Peter Malec. Markus Reiß. "Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency." Ann. Statist. 42 (4) 1312 - 1346, August 2014. https://doi.org/10.1214/14-AOS1224

Information

Published: August 2014
First available in Project Euclid: 25 June 2014

zbMATH: 1302.62190
MathSciNet: MR3226158
Digital Object Identifier: 10.1214/14-AOS1224

Subjects:
Primary: 62M10
Secondary: 62G05

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 4 • August 2014
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