## 3 Feature Selection and Forecasting Time Series
### Forecasting  
Once the FS is complete, we can begin the forecasting task in time series. Wolpert and Macready [42] stated that when we lack the information regarding the underlying model, we cannot say with certainty that any particular model will always outperform another. This means that the optimal strategy is to experiment with a number of techniques in order to discover the most effective model. This research has used both linear and non-linear techniques to focus on the algorithms that show the greatest promise. Linear regression is one of the simplest techniques. In this model, we search for an estimate of the model parameters in order to minimize the sum of the squared errors [43]. The modifications incorporate partial least squares/penalized models, e.g., ridge regression or LASSO. One advantage from the proponents of such models is that they are easy to interpret. Relationships are indicated by the coefficients and these are generally very simple to calculate, meaning that we can afford to employ a number of features. However, performance with these models may be limited [44]. Good results are achieved if the predictor/response relationship falls on a hyperplane. If we have higher-order relationships, e.g., like, cubic, or quadratic, such models may not accurately capture nonlinear relationships and thus we have to look for a different approach [45]. Certain models are capable of understanding non-linear trends. We do not need to know the precise type of nonlinearity prior to constructing our model. One of the most widely used models is Support Vector Machines (SVM). These are dual learning algorithms that compute the dot-products of data in processing [46]. Proper computation of such dot-products between variable rates may be achieved using a kernel function [47]. Using such a function, SVM learners seek out the hyperplane separating the examples with the maximum separation (margin) between them. It is recognized that SVMs are resistant to overfitting and perform well in terms of generalization as a result of the max-margin criterion employed during the optimization process. Additionally, although alternative solutions produce only local optimums, SVM will converge to a global optimum due to the corresponding convex optimization formulation [48]. There has been considerable interest in the Regression Trees family of modeling algorithms in recent times. Tree-based modeling employs if/then statements to find the predictors that will be used for data partitioning. In such subsets, a model is employed for forecasting outcomes [49]. Statistically, the addition of randomness when constructing the tree helps to reduce correlations between predictors. This is used in the Random Forests(RF) technique [50]. All models from the set are employed in building predictions for new datasets, and an average is taken of the predictions, which supplies the ultimate forecast. RF models undertake variance reductions through the selection of robust complex learners with low bias levels. This decreases the number of errors and additionally proves strong in overcoming noisy responses [51]. Gaussian Processes (GPs) with Radial Basis Function Kernels (RBF) [52] and other forms of comparative strategy create consistency overall and allow for a limitless quantity of basic functions, but these are rarely used, even though some past research has demonstrated that it can show promise [53]. GP methodology is nonparametric, with a focus on taking discernible reactions from a variety of training data points (function values) and modeling them as multivariate standard random features [54]. It is assumed that there is a priority distribution of these function data values, guaranteeing that the function will operate smoothly. When the comparing vectors are close (in the sensitivity and separation), the function values will be closely correlated, with decay occurring upon divergence. We may subsequently calculate how the unpredicted function data is distributed by employing an assumed distribution and applying a basic probability manipulation.