## 6 Results and Discussion: Forecasting Performance
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Subset FS** & **Spain** & \multicolumn{2}{c}{**Madrid**} & \multicolumn{2}{c}{**Alicante**} & \multicolumn{2}{c}{**Segovia**} \\ \hline  & \begin{tabular}{c} **Standard** \\ **(RMSE \(6\)-Steps)** \\ \end{tabular} & \begin{tabular}{c} **(RMSE \(6\)-Steps)** \\ \end{tabular} & \begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & \
\begin{tabular}{c} **(RMSE \(6\)-Steps)** \\ \end{tabular} &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline \multicolumn{6}{c}{_Forecasting technique: GP_} \\ \hline No FS. & 0.3949 & 0.0332 & 0.4966 & 0.0806 & 0.6799 & 0.0794 & 0.5454 & 0.0686 \\ MOES-LR & 0.2217 & 0.0353 & 0.3650 & 0.0664 & 0.3271 & 0.0738 & 0.3644 & 0.0682 \\ MOES-RF & 0.1722 & 0.0219 & 0.3013 & 0.0318 & 0.2602 & 0.0377 & 0.3033 & 0.0376 \\ MOES-IBR & 0.2301 & 0.0337 & 0.3709 & 0.0353 & 0.5222 & 0.0766 & 0.3788 & 0.0513 \\ Rank-LR & 0.2232 & 0.0388 & 0.3136 & 0.0378 & 0.3299 & 0.0442 & 0.3116 & 0.0321 \\ Rank-RF & 0.2205 & 0.0272 & 0.2762 & 0.0541 & 0.3192 & 0.0493 & 0.2899 & 0.0384 \\ Rank-RF & 0.3683 & 0.0371 & 0.4226 & 0.0426 & 0.6052 & 0.1130 & 0.4225 & 0.0826 \\ Rank-PCA & 0.3134 & 0.0384 & 0.3945 & 0.0716 & 0.6471 & 0.0606 & 0.4656 & 0.0939 \\ \hline
**RMSE** & **0.2680** & **0.3676** & **0.4682** & **0.3852** & **0.3852** & \\
**Average among** & **0.2826** & **0.4076** & **0.5839** & **0.6389** & **0.6389** & \\
**techniques:\(\overline{\text{RMSE}}\)** & **0.2826** & **0.4076** & **0.5839** & **0.6389** & **0.6389** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Cont. From the results shown in Table 6, valuable conclusions can be obtained. MOES-RF appears to be the best FS technique, with RF being the best forecasting algorithm. This performance is consistent and to be expected as the time-series data from each province makes up the subsets of the whole country or, seen in a different light, the analyzed data from Spain makes up the sum of the provinces. Nevertheless, we have to highlight that \(\overline{\text{RMSE}}\) is higher for each predictive technique when the province is less populated. This can be explained because, when we are considering the whole of Spain or Madrid (millions of people), the consistency of some data is flush, and in some way occasional and punctual situations are retained averaged in a big population, showing a smoother evolution of the social variables. On the other hand, with a low population, every single fluctuation stands out more, resulting in more variability in the prediction and, hence, higher error and a bigger standard deviation. This particular case can be easily appreciated by studying the table, showing that \(\overline{\text{RMSE}}\) corresponding to each technique is around three times bigger than the whole country when applied to Segovia--0.2963 to 0.7190 u/10,000 pop (Spain and Segovia, respectively) when using SVM, or 0.2680 to 0.3852 u/10,000 pop (Spain--Segovia) when using GP. To deepen this idea, we average the \(\overline{\text{RMSE}}\) of each technique by territory one more time (referred to as \(\overline{\text{RMSE}}\) in Table 6), allowing us to appreciate this evolution clearly, growing from 0.2826, 0.4076, 0.5839, and 0.6389 u/10,000 pop (Spain, Madrid, Alicante, and Segovia, respectively). Although, for the sake of simplicity, predictions are not detailed in every step of the provinces' comparison. Figure 5 shows the instance evolution or RMSE in each territory forecasting with MOES-RF (chosen as FS) and RF. As can be seen, all of the forecasting steps show the stability of RF as a predictive algorithm, although higher values and a more oscillating prediction can be observed in the case of Segovia. Considering these results and the discussion, some important conclusions can be made in the next section.