## 6 Conclusions  
Artificial neural networks (ANNs) have been (and still are) promising modeling techniques with an ever-increasing number of real-world applications. A very wide variety of ANN methods and algorithms are available; in fact, several tens of thousands of articles containing the keywords \"time series\" and \"neural networks\" can be found online. In this survey, we covered only a small and (hopefully) not-so-biased sample containing the most representative and popular ANN architectures employed for time series prediction tasks (for a small summary of surveyed studies, see Table 2). All the prototypical ANN architectures reviewed here constitute powerful, appealing machine learning techniques founded on sound mathematical and statistical principles. This is the reason why these methods work so well in many fields of study, including time series modeling and forecasting. An interesting discussion that attempts to further explain from a theoretical perspective the success and power of ANNs (using concepts from probability and physics) can be found in [PERSON] and [PERSON] [168]. Feedforward-type ANN architectures (FFNNs, RBFNs, SOMs, SVRs, etc.) are by far the most popular among all ANN architectures employed for time series prediction tasks because of their relative simplicity, universal functional approximation properties, and stability. ANN training with alternative machine learning evolutionary algorithms (PSO, GA, ABC, etc.) and combined with ensemble modeling offers an attractive framework for  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Study** & **Main Model Employed** & \begin{tabular}{c} **Time Series Forecasting** \\ **Application** \\ \end{tabular}  \\ \hline [PERSON] et al. [81] & FFNN–PSO, Elman RNN–PSO & Macroeconomic variables \\ [PERSON] et al. [6] & FFNN–PSO & Monthly transportation data \\ [PERSON] and [PERSON] [40] & FFNN ensembles & Transportation data \\ [PERSON] [85] & Bayesian NN & Wind-generated power \\ [PERSON] et al. [169] & Deep RNN & Load forecasting \\ [PERSON] and [PERSON] [53] & Elman RNN & Chaotic time series \\ [PERSON] and [PERSON] [170] & Bayesian ESN & Chaotic time series \\ [PERSON] et al. [94] & FFNN, SVR & Monthly retail sales \\ [PERSON] et al. [66] & Double SOM–RBFN & German DAX30 index \\ [PERSON] [83] & FFNN–GA & Macroeconomic and \\ [PERSON] and [PERSON] [89] & Hybrid FFNN–BP–ARIMA & Traffic flow \\ [PERSON] and [PERSON] [164] & ESN & Wireless \\ [PERSON] et al. [80] & FFNN–PSO & \begin{tabular}{c} communication signals \\ Financial data \\ Weekly sales of a \\ finance magazine \\ \end{tabular}  \\ [PERSON] and [PERSON] [87] & Bayesian FFNN–GA & \begin{tabular}{c} Weakly sales of a \\ finance magazine \\ \end{tabular}  \\ [PERSON] [41] & RBFN ensemble & \begin{tabular}{c} NASDAQ returns \\ Natural phenomena \\ (sungspots) \\ \end{tabular}  \\ [PERSON] and [PERSON] [19] & FFNN & \begin{tabular}{c} Stock market \\ index forecasting \\ \end{tabular}  \\ [PERSON] et al. [48] & RBFN & Electric load \\ [PERSON]. [PERSON] et al. [92] & FFNN–PSO & Financial data \\ [PERSON] and [PERSON] [47] & Improved RBFN & Financial data \\ [PERSON] et al. [68] & SOM–Wavelet & Satellite rainfall runoff data \\ [PERSON] et al. [90] & Ensemble ARIMA–FFNN & Monthly rainfall in Indonesia \\ [PERSON] et al. [45] & RBFN–PSO & Global financial data \\ [PERSON] and [PERSON] [171] & SVR–ESN hybrid & China Yellow River runoff \\ [PERSON] et al. [64] & Double SOM & Polish electrical load \\ [PERSON] [84] & Bayesian FFNN & \begin{tabular}{c} time series \\ Australian Financial Index \\ Natural phenomena \\ and sunspots \\ \end{tabular}  \\ [PERSON] et al. [63] & SOM, FFNN & \begin{tabular}{c} Load demand in Spain \\ electrical system \\ Urban travel time \\ \end{tabular}  \\ [PERSON] et al. [86] & Bayesian ANN & \begin{tabular}{c} Electricity demand in Britain \\ and Wales \\ \end{tabular}  \\ [PERSON] and [PERSON] [65] & SOM–AR & \begin{tabular}{c} Natural phenomena and \\ simulated data \\ Tidal level at Canada’s \\ west coast \\ \end{tabular}  \\ [PERSON] [46] & RBFN &