## 3 Results and Discussion
### IPIF Model's Results
Moreover, if the results in Tables 9 and 10 are examined, the wider the interval, the better the accuracy. Nevertheless, this IPIF is meant to decrease the uncertainty of the energy demand in order to help power systems' decision makers, so the user's knowledge must be used to balance the proposed forecaster's interval width and the model's accuracy. Even though the IPIF for \(F=1560\) satisfies the condition PICP\({}_{\alpha}>(1-\alpha)\) for all analyzed \(\alpha\) error rates, we realized that the PICP\({}_{\alpha}\) values are far from the 95% accuracy level for those error metrics which are not \(\alpha=0.05\) (see Table 9). Therefore, through balancing accuracy and interval width, the most suitable \((F,\ \alpha)\) combinations were selected. Table 11 shows the selected \(F\) parameter for each \(\alpha\) error rate as well as the corresponding error metrics not only for the sample days shown in Tables 5 and 10 but also for a few others, which were randomly chosen. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{**Date**} & \multicolumn{5}{c}{**Error Metric**} \\ \cline{3-7}  & & \(100\times\)**PIC\({}_{\alpha}\)** & \(100\times\)**CE\({}_{\alpha}\)** & \(100\times\)**NPIAW\({}_{\alpha}\)** & \(100\times\)**SS\({}_{\alpha}\)** \\  & & **(N = 98)** & **(N = 98)** & **(N = 98)** & **(N = 98)** \\ \hline  & 08/02/2018 & 98.96 & 3.96 & 11.51 & 0.36 \\  & 04/05/2018 & 95.83 & 0.83 & 9.59 & 0.47 \\ \(\alpha=0.05\) & 25/07/2018 & 98.96 & 3.96 & 12.03 & 0.38 \\ \(F=1560\) & 16/08/2018 & 95.83 & 0.83 & 8.67 & 0.31 \\ (**N = 96)** & 28/09/2018 & 97.92 & 2.92 & 13.18 & 0.44 \\  & 10/11/2018 & 95.83 & 0.83 & 6.39 & 0.24 \\  & 19/12/2018 & 96.88 & 1.88 & 11.15 & 0.36 \\ \hline  & 08/02/2018 & 98.95 & 8.95 & 11.62 & 0.72 \\  & 04/05/2018 & 95.83 & 5.83 & 10.08 & 0.77 \\ \(\alpha=0.10\) & 25/07/2018 & 100.00 & 10.00 & 12.49 & 0.79 \\ \(F=1546\) (N = 96) & 16/08/2018 & 95.83 & 5.83 & 8.94 & 0.60 \\  & 28/09/2018 & 98.96 & 8.96 & 14.15 & 0.88 \\  & 10/11/2018 & 94.79 & 4.79 & 6.34 & 0.44 \\  & 19/12/2018 & 97.92 & 7.92 & 11.32 & 0.72 \\ \hline  & 08/02/2018 & 97.91 & 12.92 & 10.81 & 1.01 \\  & 04/05/2018 & 93.75 & 8.75 & 9.55 & 0.99 \\ \(\alpha=0.15\) & 25/07/2018 & 97.92 & 12.92 & 11.83 & 1.12 \\ \(F=1540\) (N = 96) & 16/08/2018 & 92.71 & 7.71 & 8.85 & 0.88 \\  & 28/09/2018 & 96.87 & 11.87 & 13.09 & 1.20 \\  & 10/11/2018 & 91.67 & 6.67 & 6.30 & 0.63 \\  & 19/12/2018 & 96.87 & 11.86 & 11.10 & 1.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: NPIAW\({}_{\alpha}\) results for computed scenarios \((F,\ \alpha)\). The results presented in Table 11 demonstrate that, with our forecaster and a sensitivity analysis for the \(F\) parameter, it is possible to obtain IPIFFs whose accuracy is close to the stated goal of 95% in terms of the analyzed \(\alpha\) error rates maintaining interval width. If we focus on the \(\text{SS}_{\alpha}\) column, it can be seen that the bigger the \(\alpha\) error rate is, the bigger the \(\text{SS}_{\alpha}\) value is. This fact does not rely on the predicted interval width; if Equation (22) is examined, it can be seen how \(\alpha\) is taken into account in computing \(\text{SS}_{\alpha}\) values, so the higher \(\alpha\), the higher \(\text{SS}_{\alpha}\). Figures 3-5 show the predicted intervals obtained for 8 February 2018 for each examined scenario in Table 11.  
Figure 4: Predicted intervals and actual energy demand evolution for 8 February 2018 scenario (\(\alpha=0.10\), \(F=1546\)). Figure 3: Predicted intervals and actual energy demand evolution for 8 February 2018 scenario (\(\alpha=0.05\), \(F=1560\)). Figures 2-4 demonstrated that even though the error rate increases, our forecaster, with the \(F\) parameter's proper sensitivity analysis, is able to maintain high accuracy, which is close to the stated goal of 95%. In contrast to other studies in the literature, such as [PERSON] et al. [56] or [PERSON] et al.