  This paper proposes a novel multiscale estimator for the integrated
volatility of an Ito process, in the presence of market microstructure noise
(observation error). The multiscale structure of the observed process is
represented frequency-by-frequency and the concept of the multiscale ratio is
introduced to quantify the bias in the realized integrated volatility due to
the observation error. The multiscale ratio is estimated from a single sample
path, and a frequency-by-frequency bias correction procedure is proposed, which
simultaneously reduces variance. We extend the method to include correlated
observation errors and provide the implied time domain form of the estimation
procedure. The new method is implemented to estimate the integrated volatility
for the Heston and other models, and the improved performance of our method
over existing methods is illustrated by simulation studies.
