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We propose localized spectral estimators for the quadratic covariation andthe spot covolatility of diffusion processes which are observed discretely withadditive observation noise. The eligibility of this approach to lead to anappropriate estimation for time-varying volatilities stems from an asymptoticequivalence of the underlying statistical model to a white noise model withcorrelation and volatility processes being constant over small intervals. Theasymptotic equivalence of the continuous-time and the discrete-time experimentsare proved by a construction with linear interpolation in one direction andlocal means for the other. The new estimator outperforms earlier nonparametricapproaches in the considered model. We investigate its finite sample sizecharacteristics in simulations and draw a comparison between the variousproposed methods.

Spectral covolatility estimation from noisy observations using local weights