# Solar Irradiance Forecasting Using Dynamic Ensemble Selection
## 5 Experiments
### Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Series** & **MODEL** & **RMSE** & **MAPE** & **MAE** & **ARV** & **IA** \\ \hline \multirow{8}{*}{**MODEL**} & ARIMA [32; 33] & 0.0824 & 21.21 & 0.0639 & 0.1181 & 0.9705 \\  & RF [69; 70] & 0.0742 & 13.06 & 0.0563 & 0.1170 & 0.9739 \\  & GB [37; 38] & 0.0746 & 13.63 & 0.0558 & 0.1155 & 0.9739 \\  & SVR [34; 71] & 0.0629 & 12.87 & 0.0457 & 0.0695 & 0.9830 \\  & MLP [39; 72] & 0.0676 & 14.65 & 0.0516 & 0.0853 & 0.9797 \\  & ELM [40; 41] & 0.0718 & 12.95 & 0.0528 & 0.1037 & 0.9762 \\  & DBN [42; 43] & 0.0660 & 11.89 & 0.0481 & 0.0839 & 0.9803 \\  & HetDS(1,5) & 0.0626 & 11.07 & 0.0447 & 0.0689 & 0.9831 \\  & HetDS(1,10) & 0.0617 & 10.73 & 0.0436 & 0.0672 & 0.9836 \\  & HetDS(1,20) & 0.0612 & 10.67 & 0.0434 & 0.0660 & 0.9838 \\  & HetDS(3,5) & 0.0607 & 10.77 & 0.0435 & 0.0665 & 0.9839 \\  & HetDS(3,10) & 0.0605 & 10.61 & 0.0429 & 0.0659 & 0.9841 \\  & HetDS(3,20) & **0.0600** & **10.57** & **0.0426** & **0.0646** & **0.9844** \\  & HetDS(5,5) & 0.0618 & 11.31 & 0.0448 & 0.0715 & 0.9830 \\  & HetDS(5,10) & 0.0616 & 11.23 & 0.0445 & 0.0710 & 0.9832 \\  & HetDS(5,20) & 0.0616 & 11.22 & 0.0445 & 0.0708 & 0.9832 \\  & Hetmean & 0.0644 & 12.80 & 0.0479 & 0.0807 & 0.9812 \\  & Hetmedian & 0.0647 & 12.30 & 0.0477 & 0.0807 & 0.9811 \\ \hline \multirow{8}{*}{**MODEL**} & ARIMA [32; 33] & 0.1024 & 24.74 & 0.0746 & 0.2135 & 0.9478 \\  & RF [69; 70] & 0.0938 & 21.28 & 0.0671 & 0.1944 & 0.9547 \\  & GB [37; 38] & 0.0942 & 20.36 & 0.0663 & 0.1876 & 0.9553 \\  & SVR [34; 71] & 0.0962 & 20.43 & 0.0655 & 0.1754 & 0.9558 \\  & MLP [39; 72] & 0.0956 & 20.76 & 0.0667 & 0.1850 & 0.9548 \\  & ELM [40; 41] & 0.1002 & 22.44 & 0.0713 & 0.2067 & 0.9499 \\  & DBN [42; 43] & 0.0962 & 22.00 & 0.0693 & 0.1970 & 0.9531 \\  & HetDS(1,5) & 0.0955 & 20.68 & 0.0665 & 0.1840 & 0.9550 \\  & HetDS(1,10) & 0.0955 & 20.82 & 0.0670 & 0.1839 & 0.9550 \\  & HetDS(1,20) & 0.0938 & 20.52 & 0.0655 & 0.1791 & 0.9565 \\  & HetDS(3,5) & 0.0937 & 20.03 & 0.0648 & 0.1800 & 0.9564 \\  & HetDS(3,10) & 0.0934 & 19.87 & 0.0645 & 0.1788 & 0.9567 \\  & HetDS(3,20) & **0.0931** & **19.87** & **0.0643** & 0.1780 & **0.9570** \\  & HetDS(5,5) & 0.0934 & 19.97 & 0.0646 & 0.1802 & 0.9566 \\  & HetDS(5,10) & 0.0933 & 19.97 & 0.0645 & 0.1801 & 0.9566 \\  & HetDS(5,20) & 0.0933 & 19.95 & 0.0646 & 0.1805 & 0.9566 \\  & Hetmean & 0.0933 & 20.28 & 0.0648 & 0.1819 & 0.9564 \\  & Hetmedian & 0.0936 & 20.30 & 0.0650 & 0.1820 & 0.9563 \\ \hline \multirow{8}{*}{**MODEL**} & ARIMA [32; 33] & 0.1051 & 27.15 & 0.0788 & 0.2739 & 0.9398 \\  & RF [69; 70] & 0.0954 & 19.48 & 0.0657 & 0.2102 & 0.9524 \\  & GB [37; 38] & 0.0973 & 20.18 & 0.0668 & 0.2190 & 0.9504 \\  & SVR [34; 71] & 0.0902 & **17.12** & **0.0579** & **0.1581** & **0.9610** \\  & MLP [39; 72] & 0.0900 & 17.95 & 0.0601 & 0.16  
In addition, Table 4 presents the percentage difference (PD) regarding RMSE between single and ensemble models with the best proposed version of HetDS. It is possible to note that HetDS obtained a superior performance in terms of RMSE when compared to the other statistical and ML models used. Figures 4-7 show the dispersion of the results considering the 10 independent simulations by means of a boxplot graphic. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**MODEL**} & \multicolumn{5}{c}{**SERIES**} \\ \cline{2-5}  & **Fortaleza** & **Florianopolis** & **Salvador** & **São Paulo** \\ \hline ARIMA [32; 33] & 14.97 & 27.28 & 19.55 & 9.11 \\ RF [69; 70] & 6.38 & 19.16 & 1.5 & 0.72 \\ GB [37; 38] & 8.21 & 19.67 & 2.96 & 1.18 \\ SVR [34; 71] & 0.89 & 4.67 & 11.45 & 3.18 \\ MLP [39; 72] & 0.75 & 11.29 & 6.97 & 2.62 \\ ELM [40; 41] & 8.11 & 16.55 & 10.74 & 7.03 \\ DBN [42; 43] & 2.72 & 9.16 & 9.08 & 3.23 \\ Hetmean & 4.43 & 4.23 & 7.76 & 2.46 \\ Hetmedian & 5.43 & 2.88 & 4.86 & 2.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Percentage difference (%) regarding RMSE between single and ensemble models with the best proposed version of HetDS. Figure 4: Boxplot graphic regarding Fortaleza.