From 1917 to 1918, Major Arthur Hurst filmed shell-shocked patients home from the war in France. Funded by the Medical Research Committee, and using Pathé cameramen, he recorded soldiers who suffered from intractable movement disorders as they underwent treatment at the Royal Victoria Hospital in Netley and undertook programs of occupational therapy at Seale Hayne in Devon. As one of the earlie...

We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. Mathematics Subject Classification (2000). Primary 60G07; Secondary 60G15, 60G48, 60G25.

This paper is a condensed introduction to self-similarity, self-similar processes, and the estimation of the Hurst parameter in the context of time series analysis. It gives an overview of the literature on this subject and provides some assistance in implementing Hurst parameter estimators and carrying out experiments with empirical time series.

This paper presents a study of the Hurst index estimation in the case of fractional Ornstein–Uhlenbeck and geometric Brownian motion models. The performance of the estimators is studied both with respect to the value of the Hurst index and the length of sample paths.

The Hurst parameter captures the amount of long-range dependence (LRD) in a time series. There are several methods to estimate the Hurst parameter, being the most popular: the variance-time plot, the R/S plot, the periodogram, and Whittle’s estimator. The first three are graphical methods, and the estimation accuracy depends on how the plot is interpreted and calculated. In contrast, Whittle’s ...

This paper is a condensed introduction to self-similarity, self-similar processes, and the estimation of the Hurst parameter in the context of time series analysis. It gives an overview of the literature on this subject and provides some assistance in implementing Hurst parameter estimators and carrying out experiments with empirical time series.