## 5 Discussion and Conclusions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Parameters** & **MAPE (\%)** & **RMSE** & **MAE** & \begin{tabular}{c} **Directional** \\ **Accuracy** \\ \end{tabular} \\ \hline \begin{tabular}{c} Support Vector \\ Regression \\ \end{tabular} & Kernel = Polynomial degree 2, C = 8, \\ \begin{tabular}{c} Epsilon = 0.1, Gamma = 0.1 \\ \end{tabular} & 2.738 & 1208.79 & 1087.49 & 0.678 \\ \hline \begin{tabular}{c} Neural Networks \\ \end{tabular} & \begin{tabular}{c} Epochs = 250, Hidden Layer \\ Neurons = 20 \\ \end{tabular} & 0.328 & 175.35 & 133.75 & 0.68 \\ \hline \begin{tabular}{c} Random Forest \\ \end{tabular} & Trees = 80 & 0.4001 & 212.69 & 158.72 & 0.643 \\ \hline \
\begin{tabular}{c} Hybrid Model \\ \end{tabular} &
\begin{tabular}{c} Epochs = 250, Hidden Layer \\ Neurons = 3 \\ \end{tabular} & 0.439 & 231.26 & 174.06 & 0.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Prediction results for the maximum price of the Dow Jones index (five selected features). on prediction quality. RMSE and MAE assess the magnitudes of the prediction errors, while directional accuracy evaluates whether the predicted price movement direction (up or down) matches the actual movement. These results suggest that the hybrid model is capable of effectively adapting to the specific characteristics of the analyzed stock data and market index; however, due to the limited number of datasets, further validation is required to confirm its general applicability across a broader range of financial assets. It is also important to note that this study did not include a direct comparison with recent deep-learning-based forecasting models such as long short-term memory (LSTM) networks or the Temporal Fusion Transformer (TFT). These methods have demonstrated  
Figure 4: Prediction of CSRN3 stock prices: left: minimum and right: maximum. Figure 5: Prediction of CPFE3 stock prices: left: minimum and right: maximum. Figure 6: Prediction of Dow Jones Index prices: left: minimum and right: maximum. strong predictive capabilities in time series tasks but were excluded here due to their considerably higher computational requirements. Future research should consider benchmarking the proposed hybrid model against such architectures to assess relative performance in terms of both accuracy and resource efficiency. A key limitation of this study lies in the relatively narrow scope of the datasets used. Only two individual stocks (CSRN3.SA and CPFE3.SA) and one market index (DJI) were analyzed. Although these were selected based on their uses in prior benchmark studies to ensure methodological comparability, the limited dataset reduces the generalizability of the findings. Additionally, the time spans of the datasets are inconsistent: CSRN and CPFE cover the period from 2008 to 2013, while DJI spans 2018 to 2024. This temporal gap introduces macroeconomic and structural differences that may affect comparability and the interpretation of model performance across datasets. To partially address this, the DJI index was included to represent a broader international market context. Nevertheless, future research should incorporate a more diverse set of stocks from various sectors and global markets to further evaluate the robustness and scalability of the proposed hybrid model. Another important consideration relates to the assumptions inherent in the proposed approach. The model assumes that short-term price dynamics can be effectively captured using only historical price data (five previous days) and weighted moving averages without incorporating technical indicators or external features. While this choice simplifies implementation and helps prevent overfitting, it also limits the model's ability to capture sudden structural changes or external shocks. Future versions could benefit from integrating additional features, such as trading volume, volatility indices, or sectoral risk indicators. This limited feature set is another notable constraint.