Spectral Estimation of Covolatility from Noisy Observations Using Local Weights


Markus Bibinger, Institute of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany.

E-mail: bibinger@math.hu-berlin.de


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 appropriate estimation for time-varying volatilities is based on an asymptotic equivalence of the underlying statistical model to a white-noise model with correlation and volatility processes being constant over small time intervals. The asymptotic equivalence of the continuous-time and discrete-time experiments is proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier non-parametric methods in the literature for the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between various proposed methods.