Wavelet analysis of long-range-dependent traffic

TLDR

A wavelet‑based tool for analyzing long‑range dependence and estimating the Hurst parameter is introduced. The authors introduce a wavelet‑based semi‑parametric estimator of the Hurst parameter that can be efficiently implemented for large data sets, is robust to deterministic trends, is compared with traditional estimators such as Whittle, and is applied to Ethernet traffic traces to study mono versus multifractality and stationarity. The estimator is unbiased under general conditions, efficient under Gaussian assumptions, and reveals new features that impact the selection of valid models for performance evaluation.

Abstract

A wavelet-based tool for the analysis of long-range dependence and a related semi-parametric estimator of the Hurst parameter is introduced. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational, and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long-range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono versus multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.