## 4 Results and Discussion
### Comparison of ETR and Other Tree-Based Ensembles  
In this section, we delve into a comparative analysis of ETR alongside other prominent tree-based ensemble methods. Our primary objective is to provide additional insights into the performance of ETR compared to its counterparts within the context of tree-based ensemble methods in retail demand prediction. Hereby, we further want to strengthen our findings and ensure a detailed comparison of not only the selected main tree-based ensemble model, ETR, but also additional models. The selected models are as follows:  
* Random forest regressor (RFR): the RFR is another ensemble model, like ETR, which leverages a collection of decision trees to make predictions using the bagging method. It combines predictions from multiple trees to enhance accuracy and robustness. In previous research, random forests emerged as the top performer in retail sale prediction considering calendar dimensions [33];
* Gradient Boosting Regressor (GBR): the GBR is an algorithm that sequentially constructs decision trees to minimize prediction errors using the boosting method. It iteratively refines the model's predictions by focusing on correcting mistakes in subsequent iterations, leading to strong predictive performance. The GBR has been found to perform especially well in demand prediction when both numerical and categorical features are involved [53];
* XGBoost: XGBoost is another gradient-boosting algorithm known for its efficiency and high performance. It incorporates regularization techniques, parallel processing, and optimized tree construction to achieve high accuracy while maintaining computational speed. In combination with Convolutional Neural Networks (CNNs), XGBoost (XGB) was identified as the most suitable choice for predicting purchase probabilities [32].  
These ensemble models were also applied to predict demand, and the outcomes are presented in Table 4.  
Based on the evaluation results presented in Table 4, it appears that across all product categories (A, B, and C), each of the four ensemble models (ETR, RFR, GBR, and XGBoost) exhibits similar performance, indicating their consistent predictive capabilities in our use case. While there are subtle variations in the evaluation metrics among these models, in product categories A and B, ETR stands out with a slight advantage in terms of both MAPE and MAE.  
Conversely, in product category C, the GBR demonstrates a slight advantage across all metrics, including MAPE, MAE, RMSE, and R\({}^{2}\). This suggests that the GBR may be better suited for this specific category, where the underlying data patterns may be better captured by its boosting approach.  
These findings highlight the robustness and consistent performance of ensemble tree models across diverse product categories. However, it is crucial to emphasize that the choice of the most suitable model should be made carefully, considering the unique  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Product Category** & **Model Name** & **MAPE** & **MAE** & **RMSE** & **R\({}^{2}\)** \\ \hline \multirow{4}{*}{A} & ETR & 12.29\% & 1141.47 & 1794.09 & 0.60 \\  & RFR & 12.44\% & 1144.24 & 1828.58 & 0.58 \\  & GBR & 12.80\% & 1179.25 & 1816.42 & 0.58 \\  & XGBoOST & 12.68\% & 1157.18 & 1763.33 & 0.60 \\  & ETR & 12.48\% & 431.92 & 805.47 & 0.58 \\  & RFR & 12.66\% & 432.70 & 796.95 & 0.59 \\  & GBR & 13.02\% & 440.08 & 788.16 & 0.60 \\  & XGBoOST & 12.78\% & 436.63 & 789.01 & 0.60 \\  & ETR & 10.56\% & 2344.92 & 5193.20 & 0.55 \\  & RFR & 10.71\% & 2355.70 & 5215.72 & 0.54 \\  & GBR & 10.13\% & 2224.36 & 5029.83 & 0.57 \\  & XGBoOST & 10.33\% & 2269.65 & 5064.17 & 0.57 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Model evaluation results with other tree-based ensembles.  
requirements and objectives of the application. Additionally, the relative importance of different performance metrics should be carefully weighed against each other, as they can provide insights into various aspects of predictive performance.