## 3 Feature Selection and Forecasting Time Series  
### Feature Selection Techniques  
Feature selection (FS) is the process of choosing the most relevant and pertinent features from an arrangement of features in a certain given dataset. For a dataset with d input features, the feature selection process brings about k features to such an extent that k \(<\) d, where k is the smallest arrangement of critical and applicable features [33]. This results in quicker ML algorithm training, the reducing of a model's complexity so it is simpler to decipher, better forecasting power, and the decreasing of overfitting by choosing the correct arrangement of features, among others. There are three types of feature selection procedures [34]:  
- Wrapper methods  
- Filter methods  
- Embedded methods  
Wrapper methods use factor combinations to decide forecasting force. Normal wrapper strategies include: Subset Selection, Forward Stepwise Selection, and Backward Stepwise Selection (Recursive Features Elimination--RFE) [35]. The wrapper technique will locate the best mix of features, testing each variable against test models it builds with them to assess the outcomes [36]. Of the three strategies, this is more demanding computationally. In the Subset Selection strategy, we fit the model with every potential combination of N features [37]. With Forward Stepwise Selection, however, we first begin with a null model, i.e., beginning with one model variable. At this point, features are added one at a time with the best model picked depending on a metric (i.e., a valuation of the error) [36]. In this strategy, once the predictor is chosen, it never drops in the second step. This is done until the best subset of features is chosen, following a stopping criterion that establishes when the feature selection process must finish. In Backward Stepwise Selection (or Recursive Feature Elimination), the method works the opposite in that it wipes out features. As they are not run on each combination of features, they are less computationally concentrated by a significant degree when compared to straight Subset Selection [38]. Fundamentally, this is the inverse of Forward Stepwise selection. It begins with all predictors and, afterward, drops one feature at a time before selecting the best model. Likewise, the computational effort is fundamentally the same as that of Forward Selection. Filter and Wrapper strategies have been used and compared in some studies [39]. Filter methods are likewise considered as a Single Factor Analysis. By utilizing this technique, the predictive power of each individual variable (feature) is assessed, while different statistical methods can be utilized to decide predictive force [40]. One such pathway is achieved by correlating the feature with the objective (i.e., what we are foreseeing), with the features with the highest correlation being the most effective. In contrast, Embedded Method (Shrinkage) is an inbuilt variable selection strategy, within which the features are not chosen or dismissed. With this approach, some value parameter controls (weights) are carried out, making it possible to name the LASSO (Least Absolute Shrinkage and Selection Operator) Regression. With this technique, regularization is carried out and some coefficients of a regression tend to be zero [41]. Therefore, as a portion of the coefficients tends to be equivalent to zero, we can drop or reject such variables. Another example is that of Ridge Regression (Tikhonov regularization), which includes a punishment that rises to the square of the greatness of coefficients [42]. All coefficients are shrunk by the same factor (so no single predictor is eliminated). Some of these techniques will be applied in our work, in which we use a Multi-Objective Evolutionary Search Strategy [43] and also a Ranker Strategy [44], minimizing the metric that could be the Root Mean Squared Error (RMSE) and also reducing the features set. The two different types of approaches in these two groups are univariate and multivariate.