  We propose localized spectral estimators for the quadratic covariation and
the spot covolatility of diffusion processes which are observed discretely with
additive observation noise. The eligibility of this approach to lead to an
appropriate estimation for time-varying volatilities stems from an asymptotic
equivalence of the underlying statistical model to a white noise model with
correlation and volatility processes being constant over small intervals. The
asymptotic equivalence of the continuous-time and the discrete-time experiments
are proved by a construction with linear interpolation in one direction and
local means for the other. The new estimator outperforms earlier nonparametric
approaches in the considered model. We investigate its finite sample size
characteristics in simulations and draw a comparison between the various
proposed methods.
