Preliminaries on the Accurate Estimation of the Hurst Exponent Using Time Series

TL;DR

This paper investigates the minimum number of data points needed from high-speed network traffic to accurately estimate the Hurst exponent, using various estimators and validating with real network data.

Contribution

It introduces an empirical methodology to determine the minimum time series length required for accurate Hurst exponent estimation in high-speed network traffic.

Findings

Whittle estimator effectively estimates Hurst exponent with few data points

Minimum series length for accurate estimation is empirically determined

Method validated on real high-speed network traffic data

Abstract

This article explores the required amount of time series points from a high-speed computer network to accurately estimate the Hurst exponent. The methodology consists in designing an experiment using estimators that are applied to time series addresses resulting from the capture of high-speed network traffic, followed by addressing the minimum amount of point required to obtain in accurate estimates of the Hurst exponent. The methodology addresses the exhaustive analysis of the Hurst exponent considering bias behaviour, standard deviation, and Mean Squared Error using fractional Gaussian noise signals with stationary increases. Our results show that the Whittle estimator successfully estimates the Hurst exponent in series with few points. Based on the results obtained, a minimum length for the time series is empirically proposed. Finally, to validate the results, the methodology is applied to real traffic captures in a high-speed computer network.