Fast Fractional Differencing in Modeling Long Memory of Conditional Variance for High-Frequency Data
12 Pages Posted: 26 Mar 2016 Last revised: 27 Mar 2018
Date Written: March 24, 2016
In econometrics, long memory models for variance modeling like FIGARCH or FIAPARCH are characterized by a Fractional Differencing term. In order to estimate and apply these models, the infinite MacLaurin expansion of the differencing term has to be truncated at a certain level. 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. This allows to further increase the truncation lag while ensuring a feasible computation time. 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. In order to emphasize the importance for practitioners and research in risk management, we carry out different time consuming 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(infinity)-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.
Keywords: Computation Time, Fast Fractional Differencing, Fourier Transforms, Long Memory Conditional Variance, High-Frequency Data
JEL Classification: C5, C2, C6
Suggested Citation: Suggested Citation