## 3 Results and Discussion  
The mean RMSE values of the \(k=5\) imputations for each variable and each imputation method at each of the station 1 are shown in Table 4.  
Each of the cells of the indicated tables represents the average RMSE value of the RMSE values obtained in each of the \(k\) imputations with 20% of the missing values carried out for the corresponding method and variable. That is, each of the cells in Table 4 was obtained as follows:  
As an example, the results for station ST 1 for the linear imputation method are shown in Table 5. For each variable and for each imputation method, 5 RMSE values were determined, one for each \(k\) experiment with 20% missing values (cross validation with \(k=5\)) in such a way that 100% of the observations were once and only once a missing value in one of the subsets elaborated for each \(k\), \(k=1,\ 2,\dots,\ 5\). Thus, all observations were compared between their true value and their imputed value for each variable and for each imputation method. Once the RMSE values were determined for each of the k subsets that have 20% of missing values, the mean value of the method is calculated for each variable and then the mean RMSE value that determines the performance of the method at the station is found. Therefore, the mean RMSE values for each variable NO\({}_{2}\), NO\({}_{X}\), PM\({}_{10}\) and SO\({}_{2}\) at station ST 1 for the linear imputation method are, respectively, 2.0138, 6.3158, 3.4444 and 1.2751. These are incorporated in Table 5 of station ST 1 for the linear imputation method in order to be able to compare these results with the rest of the method at the same station. The mean RMSE value of all the variables obtained from the mean RMSE values of each variable is the index responsible for representing the performance of the imputation method at that station and is included in the graph in Figure A, in order to compare the imputation methods at each of the stations. In this way, by comparing the results obtained for each method and at each station, it is possible to determine which method achieves lower RMSE results at each station and, therefore, is the most suitable method for imputation of missing data for subsequent studies. By comparing the different stations with each other, it allows us to determine whether the same imputation method is suitable for all stations or whether at each station a different method should be used to better represent the missing data. The mean RMSE values of the \(k=5\) imputations for each variable and each imputation method at other stations are shown in Tables 6-11. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(\mathbf{NO_{2}}\) & \(\mathbf{NO_{X}}\) & \(\mathbf{PM_{10}}\) & \(\mathbf{SO_{2}}\) \\ \hline LI & 2.0139 & 6.3158 & 3.4445 & 1.2752 \\ PMM & 4.2221 & 12.5949 & 9.2199 & 4.1339 \\ RF & 3.9682 & 12.0137 & 9.4291 & 4.1745 \\ UMI & 6.2312 & 15.9041 & 12.7478 & 4.8826 \\ KNN & 2.9648 & 10.9477 & 8.1196 & 3.5951 \\ KALMAN & 2.0322 & 6.3102 & 3.3954 & 1.2494 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RMSE STATION ST 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**k** & \(\mathbf{NO_{2}}\) & \(\mathbf{NO_{X}}\) & \(\mathbf{PM_{10}}\) & \(\mathbf{SO_{2}}\) \\ \hline
1 & 1.9895 & 6.6772 & 3.3359 & 1.6199 \\
2 & 1.9484 & 6.5174 & 3.6770 & 1.2227 \\
3 & 1.9662 & 6.3106 & 3.3713 & 1.1784 \\
4 & 2.0774 & 5.8708 & 3.6115 & 1.2146 \\
5 & 2.0876 & 6.2029 & 3.2261 & 1.1401 \\ Mean & 2.0138 & 6.3158 & 3.4444 & 1.2751 \\ \hline \hline RMSE & 3.2623 & & & \\ \hline \end{tabular}
\end{table} 
Table 5: RMSE Linear imputation-STATION ST 1. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(\mathbf{NO_{2}}\) & \(\mathbf{NO_{X}}\) & \(\mathbf{PM_{10}}\) & \(\mathbf{SO_{2}}\) \\ \hline LI & 2.1045 & 5.9004 & 5.1703 & 1.9180 \\ PMM & 5.1576 & 13.6044 & 15.5133 & 5.9317 \\ RF & 4.6459 & 13.4225 & 15.5702 & 5.8177 \\ UMI & 7.0666 & 19.8137 & 23.4081 & 6.9183 \\ KNN & 3.4742 & 12.4591 & 14.0098 & 4.7293 \\ KALMAN & 2.0923 & 5.7102 & 5.1888 & 1.9426 \\ \hline \hline \end{tabular}
\end{table}