## 3 Feature Selection and Forecasting Time Series
### Forecasting  
After the FS is complete, the forecasting task in time series can be deployed. In 1996, [PERSON] [46] stated that, without deep information about the underlying model, there is no certain model that will always achieve better performance than any other. As a result, a proper approach can be made by trying out various techniques, then determining which model operates better. Consequently, we have compiled linear and nonlinear techniques, with a focus on the most promising algorithms. Linear Regression is one of the easiest approaches. This family of models attempts to find an estimation of the model parameters so that the sum of the squared errors is minimized [47]. Some modifications include partial least squares and penalized models such as Ridge Regression or LASSO. A significant advantage of these models is that they are highly interpretable. The coefficients indicate relationships and they are usually easy to compute, so the use of several features is affordable. On the other hand, they can be limited in their performance [48]. They achieve good results when the relationship between the predictors and their response falls along a hyperplane. However, if there are relations of a higher order, like quadratic, cubic, and alike, then the nonlinear relationships may not be properly captured with these models and so other approaches are required [49]. Some other models are capable of understanding nonlinear trends and, fortunately, the exact form of nonlinearity is not required to be known before building the model. Support Vector Machines (SVM) is of one the most popular examples in this category. These are dual learning algorithms that process data merely by computing their dot-products [50], and these dot-products between variable arrays can be properly computed by a kernel function [51]. Given this function, the SVM learner attempts to find a hyperplane that separates the examples while maximizing the separation (margin) between them. SVMs are well known to be resilient to over-fitting and to keep a good generalization performance due to the max-margin criterion used in the optimization process. In addition, while other solutions may only provide a local optimum, SVMs are guaranteed to converge to a global optimum because of the corresponding convex optimization formulation [52]. Besides this, Regression Trees make up a family of modeling algorithms that is getting a lot of attention in recent years. Tree-based models use one or more 'if-then' statements for the predictors that will subsequently partition the data. Within these subsets, a model is used to forecast the outcome [53]. From a statistical point of view, reducing correlation among predictors can be achieved by adding randomness to a tree construction process, which is the basis of the Random Forest (RF) technique [54]. Each model in the set is then used to build a prediction for a new dataset, with these predictions then being averaged to provide the final forecast. An RF model performs a variance reduction by selecting complex and strong learners that exhibit low bias. This leads to an improvement in error rates and, in addition, RF is robust to a noisy response [55]. Other comparative strategies, for example, Gaussian Processes (GPs) with Radial Basis Function Kernels (RBF) [56]--which permit an overall consistency and a non-limited number of basic functions--are infrequently utilized, albeit a few previous approaches have used this strategy with promising conclusions [57]. GPs represent a nonparametric methodology focused on modeling perceptible reactions from different training data points (function values) as multivariate normal random features [58]. A supposition is made of a priori distribution for such function data values, which will ensure the function's smoothness properties. To be explicit, there will be a high correlation between the two function values when there is closeness (in the feeling of Euclidean separation) between the comparing input vectors and if they decay as they diverge.