Fast Fractional Differencing in Modeling Long Memory of Conditional Variance Klein, Tony; Walther, Thomas We transfer the recently introduced fast fractional differencing that utilizes fast Fourier transforms (FFT) to long memory conditional variance models and show that this FFT approach offers immense speed-ups. We demonstrate how calculation times of parameter estimations of these models benefit from this new approach, relative to sample length and truncation lag. In this simulation study, allowing for higher truncation lags implies better and more precise results in parameter estimations and depiction of long memory. In order to emphasize the importance for practitioners and research in risk management, we carry out different rolling-window analyses for WTI and Brent crude oil returns and show that total computation times can be reduced by a factor 20 to 30 for FIGARCH. The speed-ups for FIAPARCH are found to be significantly higher. The FFT approach offers a computational advantage to all ARCH($\infty$)-representations of widely-used long memory models like FIGARCH, FIAPARCH, HYGARCH, and FIEGARCH, especially for large data sets which are common in high frequency analyses.