## 4 Experimental Results and Discussion
In this case, more sophisticated models obtained no better results. Nevertheless, the classical approach considers an additive relationship between the linear and nonlinear component of the time series. Consequently, this is less powerful than the other approach. For one-day ahead predictions, two different input variables (\(y\) and \(e\)) are proved sufficient to predict the time series accurately. However, there are not great differences among the prediction performances with the rest models. Similar results were obtained considering the behavior of the models for 7-day ahead prediction, where better values of performance indexes were reached with the hybrid approach 2. The most complex approach (SOM-SARIMA-SVR 2 with all variables as inputs) obtained the best results, reaching four of the five best performance indexes. Surprisingly, the classical approach SARIMA-SOM-SVR-1 is positioned as the third best model, obtaining a great MAE value. However, the results from this \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{_ph_} & **Hybrid** & \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Inputs**} & \multicolumn{5}{c}{**Performance Indices**} \\ \cline{5-10}  & & & & **R** & **d** & **MSE** & **MAE** & **MAPE** \\ \hline
1 & 1 & SOM-SARIMA-SVR 1 & \(e\) & 0.8039 & 0.8917 & 296.3551 & 11.8413 & 18.6794 \\
**1** & **2** & **SOM-SARIMA-SVR 2** & \(y\), \(e\) & **0.8101** & **0.8936** & **287.0105** & **11.6790** & 17.9391 \\
1 & 2 & SOM-SARIMA-SVR 2 & \(y\), \(p\) & 0.8024 & 0.8914 & 288.7795 & 11.7174 & **17.7721** \\
1 & 2 & SOM-SARIMA-SVR 2 & \(y\), \(e\), \(p\) & 0.8054 & 0.8919 & 287.8423 & 11.8362 & 17.8603 \\ \hline
7 & 1 & SOM-SARIMA-SVR 1 & \(e\) & 0.8037 & 0.8888 & 299.6534 & 11.9761 & 18.4053 \\
7 & 2 & SOM-SARIMA-SVR 2 & \(y\), \(e\) & 0.8051 & 0.8912 & 290.8783 & **11.8295** & 18.1178 \\
7 & 2 & SOM-SARIMA-SVR 2 & \(y\), \(p\) & 0.7906 & 0.8803 & 306.1622 & 12.4121 & 18.3690 \\
**7** & **2** & **SOM-SARIMA-SVR 2** & \(y\), \(e\), \(p\) & **0.8101** & **0.8920** & **289.7224** & 11.8394 & **17.9783** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean prediction performance results of the proposed SOM-SARIMA-SVR models for one-day and seven-day prediction horizons. The final number of the model indicates the hybrid approach (1 or 2). The column inputs indicate the inputs used in the SVR models, where \(y\), \(e\), and \(p\) represent the original data, residuals and predicted values from the second step, respectively. Best values in bold. prediction horizon do not outperform those obtained using one-day prediction horizon though the difference is not very significant. Although all the best performance indexes were gained with one-day ahead predictions, good forecasting performance were also obtained considering both prediction horizons and there exist no major differences among the hybrid approaches. Moreover, the use of a certain set of input variables from the second step (SARIMA set) does not seem to be very relevant to improve the performance of the models in the third step. This could be due to the clustering procedure of the second step, which grouped the variables with similar properties, minimizing the negative or positive impact of selecting a certain set of input variables. Nevertheless, better results in any situation were yielded using the more sophisticated models (hybrid approach 2) instead of the classical approach (hybrid approach 1). Particularly, SARIMA-SOM-SVR-2 with variables \(e\) and \(y\) as inputs of the SVR achieved the best results. It is worth mentioning that each performance index of any hybrid approach were computed using different configurations of the parameters. That is, for instance, with the SOM-SARIMA-SVR-2 model (with \(e\) and \(y\) as input variables), the configuration of the SVR parameters (\(C\), \(\varepsilon\) and \(\gamma\)) that reached the best value of \(d\) is not the same as the one obtained the better value of MAE.