## 1 Introduction  
Predictions can have great importance on various topics, like birthrates, unemployment rates, school enrollments, the number of detected influenza cases, rainfall, individual blood pressure, etc. For example, predictions can guide people, organizations, and governments to choose the best options or strategies to achieve their goals or solve their problems. Another example of the application of predictions can be found in the consumption of electrical energy to guarantee the optimal operating conditions of an energy network that supplies electrical energy to its customers [1; 2; 3; 4; 5]. A time series is a set of records about a phenomenon that is ordered equidistantly with respect to time; this is also called a forecast. Time series are used in a wide variety of areas, including science, technology, economics, health, the environment, etc. [6]. Initially, statistical models were used to forecast the future values of the time series. These models are based on historical values of the time series to extract information about patterns (trend, seasonality, cycle, etc.) that allow the extrapolation of the behavior of the time series [1]. We can identify in the literature two main classes of methodologies for time series analysis:  
* **Parametric statistical models. ** Among the traditional parametric modeling techniques, we have the autoregressive integrated moving average (ARIMA) linear models [7]. The 1970s and 1980s were dominated by linear regression models [8]. * **Nonparametric statistical models. ** Some of these techniques include the following: self-exciting threshold autoregressive (SETAR) models [9], which are a nonlinear extension to the parametric autoregressive linear models; autoregressive conditional heteroskedasticity (ARCH) models [10], which assume that the variance of the current error term or innovation depends on the sizes of previous error terms; and bilinear models [11], which are similar to ARIMA models, but include nonlinear interactions between AR and MA terms. The main difference between both classes is that the parametric model has a fixed number of parameters, while the nonparametric model increases the number of parameters with the amount of training data [12]. Although nonlinear parametric models represent an advance over linear approaches, they are still limited because an explicit relational function must be hypothesized for the available time series data. In general, fitting a nonlinear parametric model to a time series is a complex task since there is a wide possible set of nonlinear patterns. However, technological advancements have allowed researchers to consider more flexible modeling techniques, such as support vector machines (SVMs) adapted to regression [13], artificial neural networks (ANNs), and wavelet methods [14]. [PERSON] and [PERSON] [15] and [PERSON] [16] established the mathematical and conceptual foundations of ANNs, but these nonparametric models really took off in the late 1980s, when computers were powerful enough to allow people to program simulations of very complex situations observed in real life, generated by simple and easy-to-understand stochastic algorithms that nevertheless demanded intensive computing power. ANNs belong to this class of simulations since they are capable of modeling brain activity in classification and pattern recognition problems. It was demonstrated that ANNs are a good alternative to time series forecasting. In 1987, [PERSON] and [PERSON] [17] reported the first approach to modeling nonlinear time series with an ANN. ANNs are an attractive and promising alternative for several reasons:  
* ANNs are data-driven methods. They use historical data to build a system that can give the desired result [18]. * ANNs are flexible and self-adaptive. It is not necessary to make many prior assumptions about the data generation process for the problem under study [18]. * ANNs are able to generalize (robustly). They can accurately infer the invisible part of a population even if there is noise in the sample data [19].