Comparative evaluation of semiparametric long-memory estimators

Abstract

Measurements of data traffic in telecommunication networks show that the packet arrival process exhibits long-range dependence (LRD or long-memory) increments, whose parameters (namely the Hurst parameter) can be estimated and employed in statistical inference methods to evaluate the network performance (adversely affected by LRD). In the class of the semiparametric methods used for the estimation of the Hurst parameter, the more prominent ones, the local Whittle estimator and the linear wavelet estimator by Abry and Veitch, have been validated only through an asymptotic analysis, while in a more realistic setting just finite sample sizes are available. In this article, these two semiparametric estimators are evaluated for finite sample size, by employing the Cholesky decomposition method for the simulation of the long-memory process, and the related performances are analysed on a methodological basis. In both cases, a major impact on the performances is due to choices made for the parameters of the two methods, specifically the number of vanishing moments of the wavelet used in the wavelet-based estimator and the number of frequencies used in both the local Whittle and the wavelet-based estimator. Moreover, the performances of the wavelet-based estimator could be adversely affected by the failure of some assumptions that are at the basis of its statistical properties.