## 3 Data and Results
### Prediction Sections Obtained
The \(\hat{g}^{*}_{\text{u}}\) and \(\hat{g}^{*}_{f}\) curves were obtained by increasing and reducing the values of \(y^{*}\) by 3%. The standard equation: \(\hat{g}^{*}=-3.658x^{3}+2061.89x^{2}-380,298.77\)\(x+\) 23,354,382.14 ; \(R^{2}=0.9999\). Figure 5: Predictive arcs (red line) calculated from 15 June (x = 113) to 17 October (x = 237). The black circles represent all the observed values of cumulative number of cases for a seven day average. All observed \(y^{*}\) values are within the established range of \(\pm\)3% (unfavorable --favorable), except five points (in T-1, T-6, T-7, T-8, and T-9), which are milestones of the algorithm, which indicates that a new forecast curve should be calculated. In the four sections (T-2, T-3, T-4, and T-5), all the points are within the range, and new curve sections are calculated due to the algorithm restriction to limit in 14 days each section. As an initial approach to the forecast quality, the coefficient of determination \(R^{2}\) is used. The value of this coefficient \(R^{2}=0.9994\) for the arrays \(\hat{y}^{*}\) and \(y^{*}\) is the set of the nine calculated predictive sections. This indicates a very high capacity of the algorithm to replicate, with an anticipation until two weeks, the observed results. In Figure 6, the values of \(\hat{y}^{*}\) are represented as a function of those of \(y^{*}\) with very good correlation between both arrays: \(\hat{y}^{*}=0.9943y^{*}\) (\(R^{2}=\)0.9997). As expected, in each of the sections of the predictive curves, increasing x increases the relative standard errors of prediction. This can be seen very well in Figure 7, where \(e_{r}=\dfrac{(y^{*}-\hat{y}^{*})}{y^{*}}\) is plotted versus x. We also observed that between x = 127 (29 June) and x = 191 (1 September), the relative errors are in the range of \(-0.83\%\) to \(1.48\%\), and therefore, all the observed values fall between the favorable and unfavorable scenario. This fact will be interpreted later. Figure 6: Arrays of observed and forecasted values between 15 June and 17 October (\(\hat{y}^{*}\) vs. \(y^{*}\)). On the calculation day, the seven day forecasts predict the cumulative number of cases (seven day average) that will be recorded seven days later. At the same time, if we assume the hypothesis that there is a time lapse of 14 days between the infection and the cases' registration, we also obtain an approximation of the cumulative number of infections (seven day average) that occurred one week ago. In turn, the 14 day forecasts predict the cumulative number of cases (seven day average) that will be registered 14 days later, and at the same time, a nowcast is obtained that is an approximation of the cumulative number of infections that are happening today. As the cumulative number of infections are very difficult to verify, the validation of the algorithm's predictive capacity is evaluated by comparing the values of the cumulative number of cases (seven day average) observed seven and 14 days after the calculation date. In Table 2, the seven day forecasts are presented. The relative error range is (\(-0.76\%\), \(1.03\%\)), and the median is \(-0.02\). Clearly, all forecasts are inside the favorable-unfavorable scenarios margins (\(\pm 3\%\)). In Table 3, the 14 day forecasts are shown, and therefore, nowcasts are less accurate than seven day forecasts. The median of the relative errors is \(1.15\%\), and the range is (\(-3.29\%\), \(3.98\%\)). Four of the nine 14 day forecasts lie within the margin between the favorable and unfavorable scenarios. In the other five predictions, the relative error does not in any case exceeded \(\pm 4.0\%\) with respect to the standard prediction. The results of seven and 14 day forecasts are represented in Figure 8, including the margins of the favorable and unfavorable scenarios, together with the observed curve of the seven day average of the cumulative number of cases.