## 4 Experimental Results and Analysis
### Statistical Tests  
The mean absolute error of the target model (MDFFE) is 0.002753. This shows that the prediction error of the MDFFE model is very small and the prediction accuracy is very high. Paired t-tests were performed on the MDFFE model and each of the other models to assess whether the difference in error was significant. Mean error difference: The average error difference between the target model and the comparison model. The negative value indicates that the error of the MDFFE model is smaller than that of the comparison model. For example, compared with the BiLSTMModel, the average error difference of the MDFFE model is \(-0.077870\), indicating that the error of the MDFFE model is significantly lower than that of the BiLSTMModel. T-statistic: T-test statistics, the greater the absolute value, the more significant the difference. For example, the t statistic with the BiLSTMModel is \(-205.316403\), indicating a very significant difference. T-test \(p\)-value: The \(p\) value is 0, indicating that the difference is significant at the significance level of 0.05. The smaller the \(p\) value, the more significant the difference. T-test significance (\(\alpha=0.05\)): the significance of all comparison models is 'Significant', indicating that the performance of the MDFFE model is significantly better than all other models. The paired t-test results of the models are shown in Table 5.  
Figure 6: Comparison of Fitting Performance. Figure Show the fitting of the actual and predicted values of crude oil futures prices by different models and intuitively compares the prediction accuracy and stability of each model. Figure 7 shows the absolute error distribution of different models by box plot and reveals the difference of prediction accuracy of each model. The box plot comprehensively shows the concentration trend, dispersion degree, and abnormal situation of the data through the box, median line, whisker line, and outliers. The box position of the MDFFE model is the lowest, indicating that the prediction error is the smallest and the data are concentrated. The median line is at the lowest position, which further highlights its prediction accuracy advantage; the number of outliers is small, and the distribution is concentrated, indicating that the prediction stability is high. The models in the figure are arranged in ascending order of average error. The MDFFE model is located on the far left side, with the smallest average error and the highest prediction accuracy. In general, the MDFFE model is significantly superior to other models in terms of prediction accuracy and stability, showing excellent prediction performance. The results of analysis of variance (ANOVA) in Table 6 show that there are significant differences in the mean absolute error between different models. The sum of squares of C (model) is 671.944528, the degree of freedom is 8, the F value is as high as 7053.753944, and the corresponding \(p\) value is 0.0. This shows that at the significant level of 0.05, the difference between the models is extremely significant, and the greater the F value, the more significant the difference between the models. The sum of squares of residuals is  
Figure 7: Box line diagram.