Hydrologic persistence and the Hurst phenomenon

Unlike common random series like those observed, for example, in games of chance, hydrologic (and other geophysical) time series have some structure, that is, consecutive values of hydrologic time series depend on each other. A special kind of dependence observed on large timescales was discovered by Hurst half a century ago and has been known by several names such as long-range dependence, long-term persistence, or simply the Hurst phenomenon. Since then, it has been verified that this behaviour is almost omnipresent in several processes in nature (e.g., hydrology), technology (e.g., computer networks), and society (e.g., economics). The consequences of this behavior are very significant, because it increases dramatically the uncertainty of the related processes. However, even today its importance and its consequences are not widely understood or are ignored, its nature is regarded as difficult to understand, and its reproduction in hydrologic simulation is considered a hard task or not necessary. This article shows that the Hurst phenomenon can have an easy explanation and easy stochastic representation and that simple algorithms can generate time series exhibiting long-term persistence.