Fourier volatility forecasting with high frequency data and microstructure noise

We study the forecasting performance of the Fourier volatility estimator in the presence of microstructure noise. Analytical comparison and simulation studies indicate that the Fourier estimator significantly outperforms realized volatility-type estimators, particularly for high-frequency data and when the noise component is relevant. We show that the Fourier estimator generally exhibits better performance, even compared with methods specifically designed to handle market microstructure contamination.