Evaluating maximum likelihood estimation methods to determine the Hurst coefficient

A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to est imate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0 .5 < H < 1, characterizes long memory time series by quantifying the rate o f decay of the autocorrelation function. S-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is dif ficult to distinguish between fd processes and fractional Gaussian noise (f Gn) processes. Thus, the method is evaluated for estimating H for both fd a nd fGn processes. S-MLE gave biased results of H for fGn processes of any l ength and for fd processes of lengths less than 2(10). A modified method is proposed to correct for this bias. It gives reliable estimates of H for bo th: fd and fGn processes of length greater than or equal to 2(11). (C) 1999 Elsevier Science B.V. All rights reserved.