## 3 Case Study Results
### Metropolitan Lima Stations
Likewise, within the best hybrid combination model outcomes from the STA stations, the \({}^{\textbf{b}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) produced the smallest values (RMSE = 1.495, RMSPE = 1.864, MAE = 1.078, MAPE = 7.668, and CC = 0.989). Based on these results, it is concluded that the \({}^{\textbf{b}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) is the best model among the best models as well as all twenty-seven models. To confirm the dominance of models for all monitoring stations (the ATE, the CDM, the SB, and the STA) listed in Table 4, in this work, we performed the DM test on each pair of models. The null hypothesis is that the two models on the columns and rows are equally accurate, and the alternative hypothesis is that the model on the columns is more accurate than the model on the rows (using the loss-squared function). The results (\(p\)-values) of the DM test are given in Table 5 for all four stations (ATE, CDM, SB, and STA) of Metropolitan Lima. The results of the ATE station show that the final best (\({}^{\textbf{a}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\)) model within all four best models is statistically superior to the other best combination models at the 5% level of significance. However, in the CDM, the SB, and the STA stations, the final best combination models, the (\({}^{\textbf{b}}\textbf{STLD}_{\textbf{c}}^{\textbf{c}}\)), the (\({}^{\textbf{b}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\)), and (\({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\)), are statistically superior to the other best combination models at the 5% level of significance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & & & \\ \hline \hline \multicolumn{5}{c}{**ATE Station**} \\ \hline
**Models** & **RMSE** & **RMSPE** & **MAE** & **MAPE** & **CC** \\ \hline \({}^{\textbf{a}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 4.611 & 4.464 & 1.711 & 14.862 & 0.949 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 4.636 & 4.480 & 1.704 & 14.985 & 0.948 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 5.601 & 4.817 & 1.882 & 16.179 & 0.924 \\ \({}^{\textbf{a}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 5.622 & 4.906 & 1.871 & 16.081 & 0.923 \\ \hline \hline \multicolumn{5}{c}{**Campo de Marte Station**} \\ \hline
**Models** & **RMSE** & **RMSPE** & **MAE** & **MAPE** & **CC** \\ \hline \({}^{\textbf{b}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 3.637 & 11.846 & 2.356 & 20.441 & 0.978 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 3.762 & 11.689 & 2.464 & 20.847 & 0.976 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 3.746 & 11.68 & 2.458 & 20.882 & 0.976 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 3.794 & 11.906 & 2.514 & 21.323 & 0.976 \\ \hline \hline \multicolumn{5}{c}{**San Borja Station**} \\ \hline
**Models** & **RMSE** & **RMSPE** & **MAE** & **MAPE** & **CC** \\ \hline \({}^{\textbf{b}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 1.495 & 1.864 & 1.078 & 7.668 & 0.989 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 1.559 & 1.568 & 1.136 & 7.897 & 0.987 \\ \({}^{\textbf{a}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 1.535 & 1.644 & 1.118 & 7.793 & 0.987 \\ \({}^{\textbf{b}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 1.721 & 2.021 & 1.301 & 9.293 & 0.985 \\ \hline \hline \multicolumn{5}{c}{**Santa Anita Station**} \\ \hline
**Models** & **RMSE** & **RMSPE** & **MAE** & **MAPE** & **CC** \\ \hline \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 1.969 & 15.924 & 1.462 & 76.261 & 0.989 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 2.141 & 19.925 & 1.605 & 88.958 & 0.988 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 2.143 & 19.669 & 1.603 & 89.367 & 0.988 \\ \({}^{\textbf{c}}\textbf{STLD}_{\textbf{c}}^{\textbf{b}}\) & 3.190 & 21.490 & 2.298 & 95.063 & 0.972 \\ \hline \hline \end{tabular}
\end{table}