On-line estimation of the parameters of long-range dependence

An on-line version of the Abry-Veitch (see IEEE Trans. Info. Theory, vol.44, p.2-15, 1998) wavelet based estimator of the Hurst parameter is presented. It has very low memory and computational requirements and scales naturally to arbitrarily high data rates, enabling its use in real-time applications such as admission control, and avoiding the need to store huge data sets for off-line analysis. An implementation for Ethernet based on standard hardware supporting sampling rates of 1000 data points per second is described, and results of its operation presented. The performance of the estimator as a function of the length of data processed is demonstrated using simulated data.