Fast fractional differencing in modeling long memory of conditional variance for high-frequency data

Abstract

We transfer the recently introduced fast fractional differencing that utilizes fast Fourier transforms (FFT) to long memory variance models and show that this approach offers immense computation speedups. We demonstrate how calculation times of parameter estimations benefit from this new approach without changing the estimation procedure. A more precise depiction of long memory behavior becomes feasible. The FFT offers a computational advantage to all ARCH(∞)-representations of widely-used long memory models like FIGARCH. Risk management applications like rolling-window Value-at-Risk predictions are substantially sped up. This new approach allows to calculate the conditional volatility of high-frequency in a practicable amount of time.