The evolutionary design of time series forecasters is a field that has been explored for several years now. In this paper, a complete design and training of ARMA (Auto-Regressive Moving Average) and ANN (Artificial Neural Networks) models through the use of Evolutionary Computation is presented. That is, given a time series, our proposal (EDFM - Evolutionary Design of Forecasting Models) qualitatively and quantitatively identifies a competitive model to perform the forecasting task. In the qualitative phase of the model identification, EDFM identifies the variables relevant to the process: i.e. the subset of variables, within a given window width, that provides the best forecasting, following the parsimony criterion. In the quantitative phase of the identification process, all free parameters are numerically instantiated; i.e. the coefficient of the ARMA models, or the ANN weights are determined. The results show that ANN yield better forecasts than ARMA models in all the cases presented in this paper. (C) 2012 Elsevier Ltd. All rights reserved.