The Empirical Properties of Some Popular Estimators of Long Memory Processes

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, H, or the fractional integration parameter, d, in long memory time series. We compare and contrast their performance on simulated Fractional Gaussian Noises and fractionally integrated series with lengths between 100 and 10,000 data points and H values between 0.55 and 0.90 or d values between 0.05 and 0.40. We apply all 12 estimators to the Campito Mountain data and estimate the accuracy of their estimates using the Beran goodness of t test for long memory time series.Strong dependence; global dependence; long range dependence; Hurst parameter estimators

A Markov Chain based method for generating long-range dependence

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time-series measured on the internet. The process can generate a time series exhibiting LRD with known parameters and is particularly suitable for modelling internet traffic since the time series is in terms of ones and zeros which can be interpreted as data packets and inter-packet gaps. The method is extremely simple computationally and analytically and could prove more tractable than other methods described in the literatureComment: 8 pages, 2 figure

Algorithms for Linear Time Series Analysis: With R Package

Our ltsa package implements the Durbin-Levinson and Trench algorithms and provides a general approach to the problems of fitting, forecasting and simulating linear time series models as well as fitting regression models with linear time series errors. For computational efficiency both algorithms are implemented in C and interfaced to R. Examples are given which illustrate the efficiency and accuracy of the algorithms. We provide a second package FGN which illustrates the use of the ltsa package with fractional Gaussian noise (FGN). It is hoped that the ltsa will provide a base for further time series software.