Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency
Markus Bibinger, Nikolaus Hautsch, Peter Malec, Markus Reiß
The Annals of Statistics · 2014 · Volume 42 · Issue 4
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.
Keywords
62G05, 62M10, asymptotic equivalence, Asynchronous observations, high-frequency data, integrated covolatility matrix, microstructure noise, semi-parametric efficiency
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