## Example Analysis
### Analysis of Prediction Results  
In this paper, the EN-GMDH algorithm is compared with the other five algorithms to test the performance of the EN-GMDH model in short-term load forecasting. The other five algorithms are GMDH, Lasso-GMDH using lasso regression to replace the GMDH least squares part, group method of data handling based on ridge regression (RR-GMDH) using ridge regression to replace the GMDH least squares part, the back propagation  
Figure 11: Results of Mean Absolute Scaled Error (MASE) in L1 to L9. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Evaluation** & \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**L1**} & \multirow{2}{*}{**L2**} & \multirow{2}{*}{**L3**} & \multirow{2}{*}{**L4**} & \multirow{2}{*}{**L5**} & \multirow{2}{*}{**L6**} & \multirow{2}{*}{**L7**} & \multirow{2}{*}{**L8**} & \multirow{2}{*}{**L9**} \\
**Metrics** & & & & & & & & & & & \\ \hline \multirow{9}{*}{MAE} & EN-GMDH & 2.223 & 2.360 & 3.136 & 5.660 & 6.707 & 5.602 & 1.352 & 2.521 & 1.947 \\  & GMDH & 2.744 & 2.944 & 3.467 & 6.591 & 7.104 & 6.704 & 1.238 & 2.266 & 2.728 \\  & Lasso-GMDH & 4.563 & 4.766 & 3.271 & 7.768 & 8.867 & 7.515 & 1.602 & 2.816 & 2.061 \\  & RR-GMDH & 2.267 & 2.614 & 3.252 & 6.780 & 7.150 & 6.355 & 2.354 & 1.973 & 1.965 \\  & BP & 2.386 & 2.626 & 3.437 & 7.713 & 7.929 & 6.739 & 2.026 & 2.492 & 2.894 \\  & SVM & 2.369 & 2.724 & 3.252 & 5.984 & 6.500 & 6.157 & 1.579 & 2.139 & 2.046 \\ \hline \multirow{9}{*}{sMAPE} & EN-GMDH & 2.698 & 2.842 & 3.091 & 2.477 & 2.731 & 2.499 & 1.924 & 2.347 & 2.192 \\  & GMDH & 3.657 & 3.711 & 4.042 & 3.659 & 3.585 & 3.670 & 1.915 & 2.832 & 3.699 \\  & Lasso-GMDH & 5.065 & 5.274 & 4.701 & 5.437 & 4.977 & 5.223 & 3.572 & 4.615 & 4.323 \\  & RR-GMDH & 3.801 & 3.965 & 4.192 & 3.855 & 3.807 & 3.280 & 2.860 & 3.215 \\  & BP & 3.716 & 4.318 & 4.741 & 4.561 & 4.384 & 4.185 & 3.198 & 3.533 & 4.325 \\  & SVM & 3.237 & 3.489 & 3.556 & 2.959 & 3.069 & 3.074 & 1.697 & 2.362 & 2.593 \\ \hline \multirow{9}{*}{MASE} & EN-GMDH & 0.481 & 0.225 & 0.777 & 0.780 & 0.299 & 0.704 & 0.639 & 0.631 & 0.676 \\  & GMDH & 0.529 & 0.243 & 0.859 & 0.935 & 0.295 & 0.962 & 0.769 & 0.837 & 0.827 \\  & Lasso-GMDH & 0.555 & 0.364 & 0.810 & 1.084 & 0.368 & 1.078 & 0.994 & 0.924 & 0.927 \\  & RR-GMDH & 0.491 & 0.250 & 0.805 & 0.906 & 0.297 & 0.912 & 0.816 & 0.728 & 0.784 \\  & BP & 0.538 & 0.251 & 0.851 & 1.062 & 0.329 & 0.967 & 0.796 & 0.920 & 0.810 \\  & SVM & 0.513 & 0.260 & 0.805 & 0.824 & 0.270 & 0.884 & 0.680 & 0.790 & 0.692 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation Results. EN-GMDH: group method of data handling based on elastic net; RR: ridge regression; BP: back propagation; SVM: support vector machine; MAE: Mean Absolute Error; sMAPE: Symmetric Mean Absolute Percentage Err; MASE: Mean Absolute Scaled Error. Figure 10: Results of Symmetric Mean Absolute Percentage Error (sMAPE) in L1 to L9. From Figures 9-11 and Table 5, the sMAPE of EN-GMDH for load forecasting in the 8 data sets is significantly smaller than that of the other five algorithms except L7. Moreover, the MASE of EN-GMDH has obvious advantages over the other algorithms, the prediction accuracy is higher, the prediction effect is more stable, and the prediction error does not appear to fluctuate greatly. Statistical significance of the results is explored with Friedman test on the basis of sMAPE measure. It is used to determine if the distribution of the error measurement for the models used differ in this paper. The Friedman test shows an obvious significance (\(p\) = 0.0121) in the first step. We can conclude that there are differences in performance between the models, but we cannot judge in which group of models the differences exist [9; 53; 55]. Thus, the Tukey-Kramer test is used as a post-hoc procedure for further statistical tests. The test in this process is completed by the statistical function of MATLAB (R2017b, MathWorks, Natick, MA, USA, 2017) software, a significance level of \(\alpha\) = 0.05 is used.