Small Sample Properties of H and K—Estimators of the Hurst Coefficient h

Abstract

Seasonal differences in long‐term persistence (h > 0.5), were found for 25 streams in the Potomac River basin. Two statistics, H and K, used as estimators of h were found to have differing small sample properties. K was found to have less variance but a greater positive bias than H. However, the Hurst phenomenon, in which H and K values differ from the expected values for independent series, was confirmed for the Potomac River basin streamflows. Neither marginal distribution nor biased transience appear to be viable explanations for the differences between observed and independent or short memory simulated sequences. For the Potomac basin, the explanation of h > 0.5 can only be attributed to the nature of the correlation structure of the observed series.