  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
Cram\'{e}r-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.
