## 4 Results
Results are displayed by providing summary statistics in each subplot through box plots, color-coded with different colors, each representing a different time-lag (refer to the legends). Figure 7: The figure reports the forecasting performance gained for each metric when each selected feature was used as input over all the employed AutoML models. The figure reports the test set forecasting performance through five separate subplots, each corresponding to a different performance metric, previously described in Section 3.4. Results are displayed by providing summary statistics in each subplot through box plots, color-coded with different colors, each representing a different time-lag (refer to the legends). As a consequence of the found non-normality and non-homogeneity of variances, the ANOVA test could not be leveraged and, as an alternative, the Kruskal-Wallis test [64] was applied to understand if it existed any statistically significant difference among the employed AutoML models regarding the test set performance. The Kruskal-Wallis test allows the complete dropping of the normality and homogeneity of variances assumptions while requiring only the independence one. The null hypothesis of the latter test states that the medians of all the selected groups are equal, and the alternative hypothesis states that at least one group has a different median from the other ones. In the case the computed \(p\)-value is under a chosen significance level \(\alpha\) (typically \(\alpha=0.05\)), the null hypothesis is rejected, and at least one group median is statistically significantly different from the other group medians. As with the previously applied statistical tests, the Kruskal-Wallis test was applied with test groups defined by grouping the obtained model results by AutoML model and performance metric. In particular, a different Kruskal-Wallis test was performed for each metric to compare the AutoML model median performances on the same metric scale. As a result, the Kruskal-Wallis test indicated statistically significant differences in the AutoML model median performances for all the employed metrics, as all the computed \(p\)-values were inferior to the chosen significance level \(\alpha=0.05\). In particular, the \(p\)-values found by the executed Kruskal-Wallis were equal to \(p=0.00\) for all the analyzed performance metrics. Since the Kruskal-Wallis test indicated that the selected AutoML models showed statistically significantly different median performances, the Dunn post hoc test [65] was then executed to understand which specific AutoML models showed different median performances above other ones. As with the Kruskal-Wallis test, the Dunn test does not require the normality and homogeneity of variances assumptions, but only the independence one. The Dunn test is leveraged to perform multiple pairwise comparisons, and for each pair of groups being compared, the null hypothesis states that there is no difference in the central tendency, typically the median, between the two groups. On the other hand, the alternative hypothesis states that there is a statistically significant difference in the central tendency between the two groups being compared. The null hypothesis in the Dunn test is rejected when the \(p\)-value is less than a chosen significance level \(\alpha\) (usually \(\alpha=0.05\)). As with the previously applied statistical tests, the Dunn test was applied with test groups defined by grouping the obtained model results by AutoML model and performance metric. In particular, different pairwise Dunn tests were performed for each metric to compare the AutoML models' median performances on the same metric scale.