The aim of this thesis is to study the series of natural energy surging (NES) through long memory models, whose interest is to fit models capable of generating synthetic hydrological series. Time Series with long memory are defined as a series which have persistent dependence between observations separated by a long period of time. Firstly, we proceed to the exploration analysis where we found particulars of long memory time series. The models employed is this work were SARFIMA (p, d, q)x(P, D,Q)s where parameters d and D assume fractional values so as to incorporate long memory and/or cycles effects. It was also used a intensive computational technique called bootstrap in various stages, among them the construction of a non-parametric test for the significant of fractional parameters and the bootstrap in the residual models for generating synthetic hydrological series. In order verify the accuracy of the scenarios generated, statistical tests were performed for equal means, equal variance, adherence test and sequence analysis. Through these, we can conclude that the models used in this thesis could satisfactorily reproduce the history of natural energy surging available.