## 3 Results and Discussion
### So\({}_{2}\)  
The results for the SO\({}_{2}\) variable can be seen in Figure 10, with the range of mean RMSE, in relation to the stations, for each method, being lower than in the case of the NO\({}_{\text{X}}\) and PM\({}_{10}\) variables. As in the case of the other variables, the linear imputation and Kalman smoothing models are the ones that obtained the lowest mean RMSE values for all the stations, and the unconditional mean imputation method is the one with the worst performance. The lowest RMSE value is 1.24 and it was obtained for the Kalman method at station ST 1, followed by 1.27 for linear imputation, also at ST 1. However, for this variable, the highest mean RMSE value is not achieved with the unconditional mean imputation method but occurs for the PMM method at station ST 1, with a value of 9.42, which is strangely high. The rest of the stations achieved similar mean RMSE values for this method. ST 1 is the station that achieved the lowest mean RMSE value for the rest of the methods. As we have seen for each of the variables, the worst performing imputation method is UMI. This result corresponds to [60], which indicated that, in general, the UMI method is not recommended. In the existing literature, it has been observed that authors use different methods to create the training and validation sets as well as the way of performing the imputations. In a study conducted on the air quality monitoring dataset [61], it was determined that the method that achieved the best results in MAE and RMSE metrics was random forest imputation, with missing value rates of 5, 10, 20, 20, 20, 30 and 40%. In our study, the best results were obtained for the Kalman and linear imputation methods. The number of packets to be used depends on the methods selected for comparison. For example, ref. [61] used five R packages (MICE, VIM, AMELIA, missForest and missCompare) compared to the three R packages (MICE, VIM, imputeTS) used in this study, resulting in a lower computational cost. Some authors, such as those in ref. [62], divide the training and validation sets according to a 70:30 ratio and according to the assumptions they use, randomly but manually removing 50% every 21 days in each quarter to simulate the MCAR and using the RMSE as a metric. In [63], they constructed sets with missing data percentages of 10% and 25%, varying the gap lengths up to 50 h. Another study, [64], proposes a time series imputation method using deep learning, with good performance, but with the drawback that the model presents difficulties for series with seasonality, using the MAPE as a performance metric. Numerous studies, such as [44; 62; 65; 66], use various types of neural networks to perform missing value imputations. Although they can obtain high performances, they have a very high computational cost, especially for large data sets, and require powerful computational equipment. For example, a computationally powerful computer such as Intel(r) Xeon(r) E5-2650v4 equipped with 128 GB of RAM and NDIVIA TitanX GPU acceleration was used for the calculations performed in [64], while in our study, we used an HP Pavilion laptop Intel(r) Core(tm) i7 [EMAIL_ADDRESS] GHz equipped with 16 GB of RAM. In the studies, the total rate of missing data in the original data set can be very different from the rate of data presented by each variable [61]. In our study the rate of data that was removed is always the same for each variable and equal to the total once the initial purging is performed, but with the consideration that, with the same number of missing values in each variable, these correspond to different observations in each variable for each of the rounds. In [22], it is stated that linear imputation methods are not suitable because meteorology may affect the missing values. In our study, we found that this method obtains good results by replacing actual observations with missing data and imputing the same values with each imputation method at several stations and calculating the RMSE error.