## 3 Materials and Methods
### Data Preprocessing
#### 3.1.3 Feature Selection  
To further enhance the effectiveness of feature selection, this study employs the RF-RFE method to identify features that exhibit a strong correlation with medium- and long-term sales forecasts.The RF-RFE method was chosen for feature selection due to its ability to efficiently identify important features while handling high-dimensional data. Unlike traditional methods such as Lasso or decision trees, RF-RFE allows for the elimination of irrelevant features while retaining those that contribute the most to predictive performance.This makes it particularly well-suited for the model, where multiple features from diverse dimensions are used [23]. Feature selection was performed using RF-RFE, with features ranked in descending order of importance. Detailed results are shown in the Table 3.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Feature Dimension** & **Feature Variable Name** & **Feature Meaning** \\ \hline \multirow{3}{*}{Time Dimension} & \multirow{3}{*}{Seasonal feature} & Each season is assigned a fixed representative value: \\  & & 0 for winter, 1 for spring, 2 for summer, and 3 for autumn. \\  & & Holiday feature \\ \multirow{3}{*}{Geographical Dimension} & Latitude and longitude \\  & Population density \\ \multirow{3}{*}{Economic Dimension} & Consumer confidence index \\  & Consumer expenditure \\ \multirow{3}{*}{Product Dimension} & Government spending \\  & Packaging type \\ \multirow{3}{*}{Advertising frequency} & \multirow{3}{*}{Frequency of advertisements.} \\  & Advertising frequency \\ \multirow{3}{*}{Weather Dimension} & Store promotions \\  & Supply-chain delay \\ \cline{1-1}  & Rainfall days \\ \cline{1-1}  & Temperature average \\ \hline \hline \end{tabular}
\end{table}
Table 2: Feature description by dimension.  
Based on the feature importance values derived from RF-RFE, features were categorized into two groups based on their relevance to the model's predictive performance. Features with importance values below 0.05 were assigned a fixed importance value of 0.01, as they were considered weakly relevant. Features with importance values above 0.05 were retained with their original values, as they were deemed relevant to the prediction task. In the feature selection process, this categorization helped streamline the identification of key variables that significantly contribute to sales predictions, while effectively minimizing the influence of irrelevant or weakly correlated features.  
The analysis results reveal that \(S_{f}\) demonstrate the highest importance, with values is 0.42, indicating a substantial impact on the sales of this fast-moving consumer good. This is primarily due to consumer demand fluctuations during different seasons and holidays, which strongly highlight the seasonality of the product. The importance of \(G_{f}\) is 0.21; government spending affect sales indirectly by shaping market conditions and influencing consumer behavior. These changes impact variables like pricing and supply-chain dynamics, which in turn affect purchasing decisions. However, the influence of policies is typically less direct compared to more immediate factors like seasonality or promotions, resulting in moderate relevance to short-term sales forecasts. In contrast, features related to less relevant variables, such as \(K_{f}\), exhibit low importance values, often below 0.05, and are therefore excluded from further analysis.