AbstractIn many problems of regulation of water quantity and quality, a process of fundamental importance is that of cumulative sums — weighted or otherwise — of random variables forming a stochastic process. It is commonly believed that in such situations, the structure of the stochastic process is not important as long as the most important parameters remain the same. This means, for example, for a Markov process, with the same stationary distribution and the same serial correlation coefficient, the behaviour of the cumulative sums would be nearly the same. In this paper we show, by analytical methods and by simulation that this belief is erroneous, and that the structure of the input model has a significant effect, and that this effect increases with the serial correlation coeffici