## 6 Conclusions
\begin{tabular}{c} Natural phenomena and \\ financial data \\ \end{tabular}  \\ [PERSON] et al. [46] & Hybrid ARIMA–FFNN & \begin{tabular}{c} Natural phenomena and \\ financial data \\ \end{tabular}  \\ [PERSON] [88] & \begin{tabular}{c} Elman RNN–Kalman filter \\ \end{tabular}  \\ [PERSON] et al. [54] & Elman RNN–Kalman filter & \ \begin{tabular}{c} By-product gas flow in the \\ steel industry \\ Demand of products and \\ raw materials \\ \end{tabular}  \\ [PERSON] et al. [96] & ECNN &
\begin{tabular}{c} 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 producing accurate time series forecasts with associated uncertainty measures. Recurrent neural networks (RNNs) are hard to implement, but they are worth taking a look at, especially when we want to model long past time series behavior or when a time series behaves more like a chaotic dynamical system and less like a nonlinear autoregressive signal. RNN's standard training algorithm (namely, error backpropagation through time) requires intensive computing resources and has to be handled carefully in order to achieve convergence and stability. On the other hand, the echo state network (ESN) approach to time series RNN modeling offers a faster way to identify stable dynamical systems since fast and economical linear regression aimed at selecting appropriate nonlinear neural activations is at the core of ESN training. Especially in the early days (late 1980s and early 1990s), properly fitting a suitable ANN architecture to a given time series dataset in order to produce accurate forecasts was more of an art than a science. The building process of a time series ANN model relied heavily on trial and error and was very sensitive to the practitioner's previous knowledge and experience with the data at hand. These limitations, together with seemingly conflicting empirical evidence regarding the forecasting power of ANNs, gave rise to doubts and skepticism about ANN's overall ability to predict future time series values. In our opinion, the works surveyed in Section 4 define well-structured time series ANN modeling strategies that successfully address the aforementioned issues; however, work still needs to be done. Time series ANN modeling is not as well-established as traditional time series analysis due to the following:  
1. ANN modeling is still a fast-evolving field of study;
2. Further work still needs to be done in order to employ ANNs as useful tools for understanding and interpreting relationships among time series variables involved in the forecasting task at hand (opening the black box);
3. Although ensemble modeling and methods similar to the double SOM technique discussed in Section 4.4 provide solutions for quantifying the uncertainty of time series forecasts generated by ANN models, we think that work still needs to be done in order to construct statistically valid prediction intervals associated with time series point forecasts from ANN models. On the other hand, traditional statistical linear regression models are simple to understand, easy to implement and interpret, and are always at the forefront of the time series modeling literature. Unfortunately, linear modeling offers only an incomplete framework since nonlinear features in temporal data play an important role in many time series forecasting tasks. Parametric nonlinear modeling is a difficult and cumbersome activity since many arbitrary initial assumptions have to be made about the true form of the unknown underlying data-generating process.