Abstract The classical rescaled adjusted range ( R / S ) statistic is a popular and robust tool for identifying fractal structures and long-term dependence in time-series data. Subsequent to Mandelbrot and Wallis [Water Resour. Res. 4 (1968) 909] who proposed the statistic be measured over several subseries contained within the whole series length, the use overlapping vs. contiguous subseries has been a source of some debate amongst R/S theorists. This study examines the distributional characteristics of rescaled adjusted range and Hurst exponent estimates derived using overlapping vs. contiguous subseries, henceforth closing debate on the issue of relative bias due to either technique. Confidence intervals for the statistical significance of the Hurst exponent are also determined.