Two approximation methods to synthesize the power spectrum of fractional Gaussian noise

The simplest models with long-range dependence (LRD) are self-similar processes. Self-similar processes have been formally considered for modeling packet traffic in communication networks. The fractional Gaussian noise (FGN) is a proper example of exactly self-similar processes. Several numeric approximation methods are considered and reviewed, two methods are found that are able to provide a better accuracy and less running time than previous approximation methods for synthesizing the power spectrum of FGN. The first method is based on a second-order approximation. It is demonstrated that a parabolic curve can be indirectly used to approximate the power spectrum of FGN. The second method is based on cubic splines. Despite the fact that splines cannot be used directly to approximate the power spectrum of FGN, they can, however, considerably simplify the calculations while maintaining high accuracy. Both of the methods proposed can be used to estimate the Hurst parameter using Whittle's estimator. Additionally, they can be used on synthesis of LRD sequences.