## 3 Experiments and Results
### Results of Temporal Analysis  
In the temporal domain, spectral analysis allowed us to recognize different periodical behaviors for each institution. By using the periodogram, we could determine or discard the near-periodical nature of these signals, which is a good indicator of seasonality in a data series [18]. Two examplesof spectral analysis can be observed in Figure 5, where the fundamental period (\(T_{0}\)) of the analyzed signals could be obtained by taking into account the presence of a harmonic structure and then identifying its fundamental frequency. As seen in Figure 5a, there is a fundamental peak at the frequency corresponding to \(T_{0}=7.01\) days, which means that the near-periodic pattern clearly repeated every week in the short-time periodic institution (STPI) services. On the other hand, Figure 5b shows a fundamental frequency peak corresponding to \(T_{0}=12.01\) months, which clearly indicates the near-periodicity pattern of 1 year for the long-term periodic institution (LTPI) service. According to the above observed temporal distributions of the registered events, we noted that the FRIs in Quito could be divided into three categories, as described next. First, STPIs are those with a characteristic near-periodic behavior in short observation time intervals, that is, a week or a month. Police, health, and transit services can be included into this first category. Figure 6a illustrates the number of emergencies for these institutions over 2014, and Figure 6b details the month of March represented on a daily basis over the month. We can observe that Mondays usually exhibited the lowest number of events. The number of emergencies continued to increase during the other weekdays, and it reached the maximum values on weekends. Specifically, Saturday was most often the day when the peak of emergencies could be observed. This trend continued during the month and throughout the year. By comparing the plots of these three institutions, we can observe a similar behavior in terms of emergency peaks being coincident in similar days for this institution group. Figure 5: Spectral analysis of short-time periodic institution (STPI) (**a**) and long-term periodic institution (LTPI) (**b**) examples. The narrowband spectrum in both cases and the clear presence of harmonics highlight the periodic and seasonal character of these institutions. Figure 6: _Cont._  
Second, LTPIs are those with a near-periodic behavior during extended time intervals, in our case, a year. Figure 6c illustrates the emergencies corresponding to fire brigades over the years 2013 to 2016. In Figure 6d, four years are shown overlapping, and a characteristic pattern with a similar number of events can be observed during the first and last months of each year. In the third trimester, a dramatic increase in the number of emergencies can be seen, which was due to the summer season and its associated wildfire increase, according to [19]. The unusual peak of emergencies in April of 2016 corresponded to an earthquake of 5.9 degrees on the Ritcher scale that affected the country [20]. Finally, non-time periodic institutions (NTPIs) are those whose graphical representation or Fourier transform do not exhibit any periodic behavior, but rather they seem to be completely random and unrelated in terms of number of events. In our DB, RMS, military, and municipal services were included in this category. In Figure 6e we can see the emergencies that were attended during 2014 by these services, and Figure 6f shows March of 2014 represented with monthly and weekly scales. Given the near-periodicity present in both STPIs and LTPIs, it is useful to obtain their statistical temporal description, as given by the bootstrap CIs, trends, and outlier events (OEs). An OE is any observation outside of 1.5 times the interquartile range (IQR) over quartile Q3 and below quartile Q1 [21]. The time intervals considered for this analysis can be hourly, daily, weekly, monthly, or yearly. Emergencies recorded during 2014 were analyzed by overlapping the 52 weeks of the year.