Effect of Short-Term Memory on Hurst Phenomenon

The Hurst exponent of hydrologic time series is investigated after accounting for the short-term memory. Different versions of the rescaled range statistic are used in this study to investigate the rescaled range characteristics of hydrologic time series. The modified rescaled range accounts for short-term memory in a series. It is shown that, if the modified rescaled range is used, the Hurst exponent is close to 0.5 for standardized monthly series, indicating the absence of long-term memory in these series. Estimates of the Hurst exponent for annual series do not change very much when short-term memory is considered in its estimation.