## 3 Case Study Results  
This work uses hourly ozone concentration datasets from four monitoring stations: ATE, CDM, SB, and Santa Anita, in Metropolitan Lima, for the duration of three consecutive years: 2017, 2018, and 2019. Within each year, only winter days are considered. Therefore, there are 6768 data points for one station. The graphic presentation of all four stations' hourly time series can be seen in Figure 3. The descriptive statistics and non-stationary statistics (augmented Dickey-Fuller (ADF) [40] test) for all four stations' imputed hourly ozone time series and the log imputed hourly ozone time series are listed in Table 2. Hence, descriptive metrics are a collection of methods for summarising and describing the key characteristics of a dataset, such as its central tendency, variability, and distribution. These statistics give an overview of the data and aid in determining the presence of patterns and linkages. It can be seen from Table 2 that the clear effect of the log and without log time series is in terms of all descriptive statistics, especially the variance and standard deviation stabilization. To conclude, the log-filtered series has the least descriptive statistic values. In addition to the above, we check the unit root issue for all four stations' imputed hourly ozone time series and the log imputed hourly ozone time series statistically by the ADF test. The results (statistic values), listed in Table 2, suggest that both the log-filtered imputed hourly ozone time series and the log-imputed hourly ozone time series have a higher negative statistic value, which indicates that the series is stationary. Therefore, once the database addresses all the essential treatments, we proceed further, and for forecasting and model estimation purposes, the data are divided into two parts: a training part (for model fit) and a testing part (for out-of-sample forecast). The training part contains the data for 5424 h, which is about 80% of the overall data, and 1344 h are used as the out-of-sample (testing).  
To obtain the forecast for ozone concentration one step ahead of an hour using the proposed hybrid methodology time series forecasting presented in Section 2, the given steps need to be followed: first, the STL method of decomposition was used to get a long-run trend (\(\mathrm{I_{n}}\)), a seasonal (\(\mathrm{I_{n}}\)), and the residual (\(\mathrm{r_{n}}\)) of the time sub-series. Second, the previously explained three famous models of times series were used for each sub-series. Therefore,  
Figure 3: Ozone concentration in the metropolitan area of Lima (\(\mathrm{I_{n}}/\mathrm{m^{3}}\)): the hourly ozone concentration time series for ATE (1 st panel), Campo de Marte (2 nd panel), San Borja (3 rd panel), and Santa Anita (4 th panel).  
the forecast of an hour ahead was obtained by using the rolling window technique for 1344 h and the models were estimated accordingly. Finally, the ozone concentration forecasts were achieved through Equation (5). The performance measures, including RMSE, RMSPE, MAE, MAPE, and CC, are then used for the evaluation and comparative performance of the models. Therefore, the following subsections detail the results from four monitoring stations: Ate, Campo de Marte, San Borja, and Santa Anita, all located in Metropolitan Lima.