Hypothesis testing for long-term memory in hydrologic series

Memory in hydrologic time series is analyzed by testing the null hypothesis that there is only short-term memory in the series. The original and a modified versions of the rescaled range statistic are used to test the null hypothesis. When the modified rescaled range, which accounts for short-term memory in a series is used, the null hypothesis is accepted for the monthly series. This in turn indicates little evidence of long-term memory in the series. An identical conclusion is also arrived at when a second null hypothesis that the series are independent is tested by using the modified rescaled range statistic. The main conclusion from the study is that there is little evidence of long-term memory in monthly hydrologic series. However, for annual series, the evidence for lack of long-term memory is inconclusive, Mainly because the number of observations is small and the power of the test based on modified rescaled range is low with small samples. (C) 1999 Elsevier Science B.V. All rights reserved.