## 6 Conclusions
Linear models are often used indiscriminately by many practitioners, even if the predictions turn out to be unsatisfactory, which is often the case given time series nonlinear characteristics for many real-world problems. People's predisposition and willingness to ignore the limitations of traditional linear models is also an obstacle to the adoption of ANN techniques applied to time series forecasting tasks. Linear models, when used appropriately, are very effective tools. In fact, combining nonlinear methods based on ANNs with traditional linear models is a powerful and effective strategy. ESNs represent a prime example: linearly trained weights allow the ESN to select nonlinear neural activations from its reservoir. SOM models potentially offer a solution to the black-box problem associated with neural network models since their local approximation properties can be combined with linear time series modeling techniques, allowing users to study and interpret existing relationships among the response variable and some of its time-lagged values. An approach of our own to the problem of building statistically valid prediction intervals for time series point predictions generated by ANN models is outlined next: The basic idea is that, if a time series model has good generalization properties, then its forecasts will be close to actual future observations, and therefore the linear correlation coefficient between forecasts and true future observations (once they become available) will be close to one. Under these circumstances, it makes sense to build a simple linear re gression model (called an auxiliary linear model) using validation data (i.e., the most recent observations in the training set) as the response variable \(\gamma_{t}\) and corresponding predictions from a fully trained ANN model (called the main ANN model) as the independent variable \(X_{t}\). Under favorable circumstances, the auxiliary linear model, after being built, would have a statistically insignificant intercept coefficient \(\beta_{0}\) close to zero and a statistically significant slope coefficient \(\beta_{1}\) close to one. The residuals from the auxiliary linear model would contain valuable information about the distribution of prediction errors associated with point forecasts generated by the main ANN model. Finally, we would employ our auxiliary linear model to compute standard errors associated with point forecasts generated by the main ANN model. These standard errors would be the basis for building prediction bands with a user-defined confidence level. In an upcoming paper, we will discuss our idea in more detail, putting to the test the associated hypotheses outlined here. The recent big data phenomenon is now motivating researchers to take a closer look at machine learning techniques, specifically ANNs, which are well suited to huge time series datasets. Terabytes of satellite imaging data pour in constantly and incessantly. Such huge volumes of data would be impossible to analyze by traditional means. Machine learning techniques, including ANNs, become an essential tool in these situations since ANNs are good at identifying recurring patterns occurring in large volumes of data. The joint use of ANN and linear models applied to very large datasets with temporal structure could be a good opportunity for unifying traditional statistics and machine learning. Efforts should be made to standardize notation and techniques from both disciplines, so machine learning can be regarded by scientists and practitioners as an integral and important part of statistics.