We propose a new estimator of multivariate ex-post volatility that is robust to microstructure noise and asynchronous data timing. The method is based on Fourier domain techniques, which have been widely used in discrete time series analysis. The advantage of this method is that it does not require an explicit time alignment, unlike existing methods in the literature. We derive the large sample properties of our estimator under general assumptions allowing for the number of sample points for different assets to be of different order of magnitude. The by-product of our Fourier domain based estimator is that we have a consistent estimator of the instantaneous co-volatility even under the presence of microstructure noise. We show in extensive simulations that our method outperforms the time domain estimator especially when two assets are traded very asynchronously and with different liquidity and when estimating the high dimensional integrated covariance matrix.
