# Space-Time Prediction of PM\({}_{2.5}\) Concentrations in Santiago de Chile Using LSTM Networks
## 4 Pre-Processing of Data and Selection of Neural Model
### Analysis and Pre-Processing  
Once the information of each station was stored, the first data pre-processing step was carried out, where the normalization of the meteorological and pollutant variables corresponding to the date and time of capture was implemented. Table 2 describes the meaning of each of the variables. It is relevant to indicate that the time series that make up the database consider a time step of one hour, which was used in all the experiments carried out. Once the variables were selected, the appropriate consecutive years were considered as training and testing sets. Using the data provided and considering the percentage of missing values per year (less than 5%), the years 2012 and 2013 were considered in our experiments. Unfortunately, in the 2010-2011 period, not all of the 11 stations indicated yet existed. On the other hand, in 2014 and 2015, some stations were not operational, or measurements of some pollution variables such as NO\({}_{2}\) were not recorded. This generated discontinuity for using later years. Given that the time series require that the study period be contiguous and that we propose using the maximum number of operating stations, 11, the two indicated years were chosen. We hope in a later study to be able to incorporate a greater number of years considering at least approximate data from the stations with missing data using more complex data imputation models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**PM\({}_{2.5}\) (a)**} & \multicolumn{4}{c}{**Wind Speed (a)**} \\ \hline
**Date** & **Hour** & **(H:M) (c)** & **(d)** & **...** & **Date** & **Hour** & **(H:M) (c)** & **(d)** \\ \hline
1 January 2010 & 00:00 & 65 &... & 1 January 2010 & 00:00 & 2.20 \\
1 January 2010 & 01:00 & 70 &... & 1 January 2010 & 01:00 & 1.93 \\
1 January 2010 & 02:00 & 41 &... & 1 January 2010 & 02:00 & 1.27 \\... &... &... &... &... &... &... \\
31 December 2018 & 23:00 & 75 &... & 31 December 2018 & 23:00 & 2.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic structure of meteorological and pollutant data. \begin{table}
\begin{tabular}{l l} \hline \hline
**Variable** & **Description** \\ \hline Station & Register the name of the station \\ E & East coordinate (UTM) \\ N & North coordinate (UTM) \\ Year & Year of registration of the observation \\ Month & Observation registration month \\ Day & Observation record day \\ Hour & Observation record time \\ N\({}^{\circ}\) of week & Records the week number(1–52) \\ N\({}^{\circ}\) of day & Register day of the week (1–7) from Monday \\ type of day & Register if weekend (0–1) \\ \hline Season & \multicolumn{2}{l}{Record the season of the year (1–4) from Summer} \\ year & \multicolumn{2}{l}{Record the value of the observation} \\ \hline hrel, NO\({}_{2}\), temp \\ PM\({}_{10}\), dirv, & \multicolumn{2}{l}{Record the value of the observation} \\ velv and PM\({}_{2.5}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of the columns once the first pre-processing step was carried out. Given that we only have two years available according to the stated requirements, in our experiments we considered the out-of-sample approach, where an initial dataset formed the training set and the final data corresponded to the test set [47]. As previously indicated, in future works we plan to use more years with which even more exhaustive evaluation schemes could be considered, such as blocked cross-validation [47]. In relation to the experiments and following the out-of-sample approach, the year 2012 was selected as the training set, covering a total of 96,624 observations, and the year 2013 was used for the test set, covering a total of 96,360 observations. The difference in observations between these two datasets is due to the fact that 2012 is considered a leap year, giving an additional 24 h of observations for each of the stations. Note that the complete year is considered in each set because the information of the past months or seasons (winter or summer) can be relevant in the prediction.