## 3 Experiments and Results
### Statistical Analysis of the Best Fitted Methods
For the _utilities sector_, the analysis reflected stable behavior without apparent variation when exogenous information was incorporated. For this sector, results were outstanding in terms of the mean and the STD. The analysis of the results obtained for the different markets showed visible differences in behavior when grouped in emerging and consolidated markets. In particular, independence was noticeable in emerging markets when the presence of exogenous features was considered. The slight improvement in both the mean and the STD of the prediction error when exogenous variables were included, outlined the noticeable independence in of this market from contour variables. However, different results were found in consolidated markets. The analysis of over 30 years historical data for countries such as Japan, Spain and the USA (addressed jointly hereafter as the consolidated markets) showed that the incorporation of exogenous variables improved the predictive capability, as it was found reduced in terms of the mean and to some extent in the prediction variance. Nevertheless, noting the unequal accomplishment of the models for these two market groups, the bagtree performed better for emerging markets (Brazil, and India), whereas the winning method for consolidated region was GPR. \begin{table}
\begin{tabular}{l l c c c c} \hline \hline  & & \multicolumn{3}{c}{**Endogenous**} & \multicolumn{2}{c}{**Endo.\&Exo.**} \\  & & \(\mu\) & \(\sigma\) & \(\mu\) & \(\sigma\) \\ \hline \multirow{3}{*}{**All**} & **Bagtree** & 5.74 & 0.52 & 4.75 & 0.53 \\  & **SVR** & 6.21 & 0.58 & 5.43 & 0.53 \\
**Companies** & **GPR** & 6.16 & 0.48 & 4.88 & 0.64 \\ \hline \multirow{3}{*}{**Consumer**} & **Bagtree** & 3.93 & 0.46 & 3.46 & 0.49 \\  & **SVR** & 3.91 & 0.47 & 3.62 & 0.45 \\  & **GPR** & 3.97 & 0.48 & 3.32 & 0.45 \\ \hline \multirow{3}{*}{**Consumer**} & **Bagtree** & 5.88 & 0.74 & 5.38 & 0.56 \\  & **SVR** & 6.35 & 0.74 & 6.15 & 0.74 \\  & **GPR** & 6.16 & 0.80 & 5.51 & 0.49 \\ \hline \multirow{3}{*}{**Industrial**} & **Bagtree** & 5.23 & 2.03 & 5.72 & 2.30 \\  & **SVR** & 5.64 & 2.11 & 6.01 & 2.37 \\  & **GPR** & 6.55 & 2.32 & 6.79 & 2.06 \\ \hline \multirow{3}{*}{**Technology**} & **Bagtree** & 9.17 & 3.68 & 8.00 & 3.22 \\  & **SVR** & 9.19 & 3.61 & 8.09 & 3.26 \\  & **GPR** & 9.80 & 3.84 & 6.95 & 3.92 \\ \hline \multirow{3}{*}{**Utilities**} & **Bagtree** & 1.54 & 0.35 & 1.56 & 0.37 \\  & **SVR** & 1.34 & 0.29 & 1.37 & 0.33 \\  & **GPR** & 1.39 & 0.41 & 1.44 & 0.44 \\ \hline \multirow{3}{*}{**Brazil**} & **Bagtree** & 3.16 & 0.45 & 2.94 & 0.45 \\  & **SVR** & 3.03 & 0.50 & 3.03 & 0.50 \\  & **GPR** & 3.14 & 0.54 & 3.09 & 0.60 \\ \hline \multirow{3}{*}{**India**} & **Bagtree** & 7.11 & 2.04 & 6.66 & 1.87 \\  & **SVR** & 6.76 & 2.02 & 6.84 & 1.88 \\  & **GPR** & 7.14 & 1.97 & 7.64 & 1.71 \\ \hline \multirow{3}{*}{Japan} & **Bagtree** & 6.72 & 3.43 & 6.70 & 3.54 \\  & **SVR** & 6.57 & 3.01 & 6.42 & 3.11 \\  & **GPR** & 8.22 & 3.29 & 4.80 & 2.91 \\ \hline \multirow{3}{*}{**Spain**} & **Bagtree** & 3.17 & 0.43 & 2.76 & 0.40 \\  & **SVR** & 3.22 & 0.50 & 3.34 & 0.52 \\  & **GPR** & 3.27 & 0.50 & 2.21 & 0.39 \\ \hline \multirow{3}{*}{**USA**} & **Bagtree** & 5.36 & 0.56 & 4.51 & 0.52 \\  & **SVR** & 5.47 & 0.71 & 5.40 & 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analysis of one-hundred realizations of the best performing models, for different input-space subset scenarios. In rows, industries and region subsets. In columns, mean (\(\mu\)) and STD (\(\sigma\)) of RMSE, for the scenarios including (i) endogenous variables, and (ii) both endogenous and exogenous variables.