## 3 Case Study Results
### Metropolitan Lima Stations

Table 4: Ozone concentration in four Metropolitan Lima stations (\(\upmu\)g/m\({}^{3}\)): mean forecast error of one-hour-ahead post-sample for the best four models among all twenty-seven models. Once the proposed hybrid time series combination models' performance was evaluated by accuracy performance measures (RMSPE, RMSE, MAE, MAPE, and CC) and a statistical test (the DM test), we then processed the models for graphic analysis. For instance, a graphical representation of mean errors (RMSE, RMSPE, MAE, and MAPE) for all twenty-seven models is shown in Figure 4a for the ATE station, Figure 4b for the CDM station, Figure 4c for the SB station, and Figure 4d for the STA station. From Figure 4a-d, we can see that within all twenty-seven models, the \({}^{\textbf{c}}\)**STLD\({}^{\textbf{b}}_{\textbf{c}}\)** model in the ATE station, the \({}^{\textbf{c}}\)**STLD\({}^{\textbf{b}}_{\textbf{c}}\)** model in the CDM station, the \({}^{\textbf{c}}\)**STLD\({}^{\textbf{b}}_{\textbf{c}}\)** model in the SB station, the \({}^{\textbf{c}}\)**STLD\({}^{\textbf{b}}_{\textbf{c}}\)** model in the STA station produce the highest accuracy measures (RMSE, RMSPE, MAE, and MAPE) in comparison to the rest of all combination models. On the other hand, from all twenty-seven models in each monitoring station, the best four hybrid combination models are selected for comparison and compared with other models in each station. The results of all these best hybrid combination models are plotted in Figure 5. For example, see the ATE station in Figure 5a, the CDM station in Figure 5b, the SB station in Figure 5c, and the STA station in Figure 5d It can be observed from these plots that the \({}^{\textbf{a}}\)**STLD\({}^{\textbf{b}}_{\textbf{c}}\)**, \({}^{\textbf{a}}\)**STLD\({}^{\textbf{b}}_{\textbf{c}}\)**, and \({}^{\textbf{a}}\)**STLD\({}^{\textbf{b}}_{\textbf{c}}\)** show the least mean errors, respectively. In addition to the above, we plot the scatter diagrams for each station using their respective best model, which were obtained previously. For instance, Figure 6 displays the scatter plots for all considered monitoring stations. This figure showed that the best model produces greater correlation coefficient values, and it indicates that the correlation between forecast and actual ozone concentration values is highly significant. In the same way, the forecasted and observed values for the supermodel in each monitoring station are plotted in Figure 7. In Figure 7, forecasts of the best models follow the observed concentration of ozone very closely; from this, we can conclude that the supermodel in each considered station has accurate and efficient forecasts. Thus, from the descriptive statistical analysis, tests, and graphical results, we can conclude that the proposed hybrid combination of time series models is highly efficient and accurate in forecasting hourly ozone concentration. Figure 4: Ozone concentration (\(\mu\)g/m\({}^{3}\)) in four Metropolitan Lima stations: (**a**) ATE, (**b**) Campo de Marte, (**c**) San Borja, and (**d**) Santa Anita; the RMSPE (1 st panel), MAPE (2 nd panel), MAE (3 rd panel), and RMSE (4 th panel) for all twenty-seven combination models using the proposed forecasting methodology. Figure 5: \(Cont.\)  
Figure 5: Ozone concentration in four Metropolitan Lima stations (\(\mathrm{\SIUnitSymbolMicro g}/\mathrm{m}^{3}\)): (**a**) Ate, (**b**) Campo de Marte, (**c**) San Borja, and (**d**) Santa Anita evaluation measures; the barplot for the best four models among all twenty-seven models. Figure 6: Correlation plots for the ozone concentration (\(\mathrm{\SIUnitSymbolMicro g}/\mathrm{m}^{3}\)) in all four Metropolitan Lima stations using their respective best hybrid models, including (**1 st**) ATE (\(\mathbf{{}^{a}STLD_{c}^{b}}\)), (**2 nd**) Campo de Marte, (\(\mathbf{{}^{b}STLD_{c}^{c}}\)), (**3 rd**), San Borja (\(\mathbf{{}^{b}STLD_{c}^{b}}\)), and (**4 th**) Santa Anita (\(\mathbf{{}^{c}STLD_{c}^{b}}\)).