## 3 Results and Discussion
### PPF Model's Results
#### 3.1.5 Discussion of PPF Model  
To more easily compare the results obtained by each computed PPF model, Table 8 summarizes each model's obtained error metrics and the improvement in percentage when the results are compared against the persistence model (benchmark). For each model shown in Table 8, the value outside the brackets is the result obtained for each error metric, whereas the value inside the brackets, expressed in percentage, refers to the improvement when the values are compared against persistence benchmark. For this reason, the persistence model does not have any value inside the brackets.  
Based on the results shown in Table 8, and taking into account its easier implementation and lower computational cost not only for the training step but also in producing forecasting values, the 15-neuron FFNN structure was selected. The predictions produced  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Solver**} & \multirow{2}{*}{**Kernel Function**} & **Training** & **Validation** \\  & & **RMSE (MW)** & **RMSE (MW)** \\ \hline \multirow{3}{*}{Sequential Minimal Optimization (SMO)} & Linear & 0.1062 & **0.0951** \\  & Gaussian & 0.1187 & 0.1682 \\  & Radial basis & 0.1182 & 0.1619 \\  & Polynomial & **0.1037** & 0.0984 \\ \hline \multirow{3}{*}{Iterative Single Data Algorithm (ISDA)} & Linear & 0.1117 & 0.1008 \\  & Gaussian & 0.1183 & 0.1650 \\  & Radial basis & 0.0939 & 0.1711 \\  & Polynomial & 0.1061 & 0.1016 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Analyzed SVM structures’ averaged results for fixing solver and kernel function parameters.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **RMSE Train. (MW)** & **RMSE Val. (MW)** & **R\({}^{2}\) Train. (-)** & **R\({}^{2}\) Val. (-)** \\ \hline Value & 0.1037 & 0.0951 & 0.9926 & 0.9937 \\ Improve (\%) & 17.30\% & 24.46\% & 0.29\% & 0.49\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Computed RMSE and R\({}^{2}\) index values for optimal SVM model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **RMSE Train. (MW)** & **RMSE Val. (MW)** & **R\({}^{2}\) Train. (-)** & **R\({}^{2}\) Val. (-)** \\ \hline \multirow{2}{*}{Persistence} & 0.1254 & 0.1259 & 0.9897 & 0.9889 \\  & (-) & (-) & (-) & (-) \\ \hline \multirow{2}{*}{FFNN} & 0.0853 & 0.0766 & 0.9955 & 0.9959 \\  & (31.98\%) & (39.15\%) & (0.59\%) & (0.71\%) \\ \hline \multirow{2}{*}{RNN} & 0.0883 & 0.0766 & 0.9949 & 0.9959 \\  & (29.58\%) & (39.15\%) & (0.53\%) & (0.71\%) \\ \hline \multirow{2}{*}{SVM} & 0.1037 & 0.0951 & 0.9926 & 0.9937 \\  & (17.30\%) & (24.46\%) & (0.29\%) & (0.49) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Computed RMSE and R\({}^{2}\) index values for each model’s optimal architecture.  
by this forecaster were then used as the baseline in the proposed IPIF. If FFNN results are compared against other PIF studies in the literature, a slight improvement is obtained by the developed energy demand forecaster. For instance, [PERSON] et al. (2018) developed a VST energy demand IPIF whose FFNN forecaster's parameters were completely different to the parameters chosen in this study. In terms of R\({}^{2}\) index, [PERSON] obtained a regression value of 0.91, whereas the value obtained through this study was 0.99, demonstrating that the point forecaster slightly improves [PERSON]'s PPF.