## 4 Experimental Results and Analysis
### Quantitative Analyses  
Figure 4 shows the comparative experimental results of multiple evaluation indicators through the dot line diagram. In the (**a**) part, MAE, RMSE, and MAPE indicators show that the MDFFE model performs well, and its corresponding line trend and relative position are significantly lower than other models. This intuitively shows that the MDFFE model has significant advantages in MAE, RMSE, and MAPE. On the contrary, the LSTM model and the LSTMTransformer model perform poorly in these three indicators, and the lines are located at a higher position, indicating that the prediction error is large. The lines of other models, such as BiLSTMModel, CNN, CNNLSTM, CNNBiLSTMGRU, and TransformerModel, are between the two, showing certain predictive ability, but not as good as the MDFFE model. In the R-Squared index of part (**b**), the lines corresponding to the MDFFE model show that it has an excellent fitting effect on the data and is located at the highest position, which indicates that the model can highly explain the variability of the data. However, the LSTM model and the LSTMTransformer model have a poor fitting effect, and the lines are at a low position. In the SSE index of part (**c**), the lines of the MDFFE model show that its cumulative error is the smallest and at the lowest position, which again confirms the accuracy and stability of the MDFFE model prediction. Table 3 shows the quantitative analysis results of comparative experiments of various models in the crude oil and hot-rolled coil futures price prediction task. These models include BiLSTMModel, CNN, CNNLSTM, LSTM, CNNBiLSTMGRU, TransformerModel, LSTMTransformer, CNNLSTMGRU, and the MDFFE model proposed in this study. The evaluation indicators cover MAE\(\downarrow\), RMSE\(\downarrow\), MAPE\(\downarrow\), R-Squared, and SSE\(\downarrow\). The best results are highlighted in bold. In the task of crude oil and hot-rolled coil futures price prediction, the MDFFE model shows comprehensive and significant advantages in MAE, RMSE, MAPE, R-Squared, and SSE. The MAE value of the MDFFE model is 0.0068, which is much lower than all other  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Description** & **Key Parameters** & **Training Method** \\ \hline \multirow{4}{*}{TransformerModel} & A Transformer-based sequence model. & Input dimension: 2100, embedding dimension: 32, number of layers: 4, attention heads: 8, feed-forward dimension: 128, dropout: 0.1, and output dimension: 1. & Optimizer: Adam, learning rate: 0.001, epochs: 50, batch size: 128, and seed: 666. \\ \cline{2-4}  & A hybrid model combining LSTM and Transformer layers. & Input dimension: 2100, LSTM layers: 4, Transformer layers: 4, embedding dimension: 32, and output dimension: 1. & Optimizer: [PERSON], learning rate: 0.001, epochs: 50, batch size: 128, batch size: 128, and seed: 666. \\ \hline \multirow{4}{*}{CNNLSTMGRU} & A hybrid model combining CNN, LSTM, and GRU layers. & Input dimension: 2100, CNN layers: 2, LSTM hidden layer dimension: 64, layer dimension: 64, and output dimension: 1. & Optimizer: [PERSON], learning rate: 0.001, epochs: 50, batch size: 128, batch size: 128, batch size: 128, and seed: 666. \\ \cline{2-4}  & A hybrid model combining CNN, LSTM, and GRU layers. & Input dimension: 2100, CNN layers: 2, LSTM hidden layer dimension: 64, layer dimension: 64, layer dimension: 64, layer dimension: 64, layer dimension: 64, and output dimension: 1. & Optimizer: [PERSON], learning rate: 0.001, epochs: 50, batch size: 128, batch size: 128, and seed: 666. \\ \hline \multirow{4}{*}{MDFFE} & A hybrid model combining CNN, LSTM, and GRU layers. & CNN output dimension: 128, XGBoost parameters: number of trees: 200, number of trees: 200, learning rate: 0.001, epochs: 50, batch size: 128, and seed: 666. \\ \cline{1-1} \cline{2-4}  & A hybrid model combining CNN for feature extraction & CNN output dimension: 128, XGBoost parameters: number of trees: 200, learning rate: 0.001, learning rate: 0.001, epochs: 50, batch size: 128, and seed: 666.