## 3 Case Study Results
### Metropolitan Lima Stations  
This subsection elaborates on the results and discussion about the Metropolitan Lima station. First, the hourly time series of the ATE, the CDM, the SB, and the SBA station's ozone concentration (\(\epsilon_{n}\)) are decomposed into a long-run trend (\(t_{n}\)), seasonal (\(b_{n}\)) and a residual sub-series (\(r_{n}\)); the STL decomposition method was implemented in this study. For obtaining the forecasts of the sub-series, three univariate time series models were used. Ensemble models for sub-series forecast of (\(3^{t_{n}}\times 3^{t_{n}}\times 3^{r_{n}}=27\)) different combinations for all four considered monitoring stations were used. For these 27 different combination models, the performance measures (RMSE, RMSPE, MAE, MAPE, and CC) for one hour ahead of out-of-sample forecasts for the ATE, the CDM, the SB, and the SBA stations are listed in Table 3.  
In the first attempt, the case study results of the ATE station accuracy performance measures (RMSE, RMSPE, MAE, MAPE, and CC) show that the \({}^{\mathbf{a}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** hybrid combination model produces the best forecasts compared to all other possible hybrid combinations of time series models. The \({}^{\mathbf{a}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** is the best forecasting model, which produced 4.611, 4.464, 1.711, 14.862, and 0.949 for RMSE, RMSPE, MAE, MAPE, and CC, respectively. However, the \({}^{\mathbf{c}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** (4.636, 4.480, 1.704, 14.985, 0.948), \({}^{\mathbf{c}}\)**STLD\({}_{\mathbf{b}}^{\mathbf{b}}\)** (5.601, 4.817, 1.882, 16.179, 0.924), and \({}^{\mathbf{a}}\)**STLD\({}_{\mathbf{b}}^{\mathbf{b}}\)** (5.622, 4.906, 1.871, 16.081, 0.923) models produced the second, third, and fourth best results. Similarly, in the second attempt, the case study results of the CDM station and the results of the performance accuracy measures show that the \({}^{\mathbf{b}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** model yields better forecasts compared to all other possible hybrid combination models. The best forecasting model, \({}^{\mathbf{c}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{c}}\)**, produced 3.637, 11.846, 2.356, 20.441, and 0.978 for RMSE, RMSPE, MAE, MAPE, and CC, respectively. However, the \({}^{\mathbf{c}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** (3.762, 11.689, 2.464, 20.847, 0.976), \({}^{\mathbf{a}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** (3.746, 11.68, 2.458, 20.882, 0.976), and \({}^{\mathbf{c}}\)**STLD\({}_{\mathbf{b}}^{\mathbf{b}}\)** (3.794, 11.906, 2.514, 21.323) models produced the second, third, and fourth best results. In the same way, in the third attempt, the case study results of the SB station and the results of the performance accuracy measures show that the \({}^{\mathbf{b}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** model yields better forecasts compared to all other possible combination models. The best forecasting model is \({}^{\mathbf{b}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)**, which gives outcomes of 1.495, 1.864, 1.078, 7.668, and 0.989 for RMSE, RMSPE, MAE, MAPE, and CC, respectively. However, the \({}^{\mathbf{c}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** (1.559, 1.568, 1.136, 7.897, and 0.987), \({}^{\mathbf{a}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** (1.535, 1.644, 1.118, 7.793, and 0.987), and \({}^{\mathbf{b}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** (1.721, 2.021, 1.301, 9.293, and 0.985) models produced the second, third, and fourth best results. Finally, in the fourth attempt, the case study results of the SB station and the results of the performance accuracy measures show that the \({}^{\mathbf{c}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)** model yields better forecasts compared to all other possible combination models. The best forecasting model is \({}^{\mathbf{c}}\)**STLD\({}_{\mathbf{c}}^{\mathbf{b}}\)**, which gives outputs of 1.969, 15.924, 1.462, 76.261, and 0.989 for RMSE, RMSPE, MAE, MAPE, and CC, respectively.