This article aims at investigating two different methodologies to forecast time series of river flows. Models originated from Box & Jenkins method, as well as models based on artificial neural networks technique have been constructed. The proposed models were used in order to forecast future values of the historical series of Rio Grande’s natural flows. The time series data have been collected from the stream gauge station of Madre de Deus de Minas, MG. Afterwards, a comparative analysis between both techniques used at the prognostication of time series has been done. The results obtained from the comparison have shown that each methodology can be adequately adjusted to the set of studied observations; however, each technique has advantages and disadvantage.