## 5 Conclusions  
Prediction tasks and forecasting methodologies and models are constantly evolving. Diverse methodologies to address forecasting problems have been proposed with mixed results, highlighting \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(ph\)} & \multirow{2}{*}{**Model**} & \multicolumn{6}{c}{**Performance Indices**} \\ \cline{3-6}  & & \(R\) & \(d\) & _MSE_ & _MAE_ & _MAPE_ \\ \hline \(1\) & SVR & 0.7989 & 0.8836 & 389.1624 & 14.3328 & 23.0695 \\ \(1\) & SOM-SVR & 0.8042 & 0.8862 & 381.6965 & 14.1565 & 21.8681 \\ \(1\) & SARIMA-SVR & 0.8048 & **0.8952** & 302.0054 & 12.0024 & 19.4246 \\ \(\mathbf{1}\) & **SOM-SARIMA-SVR** & **0.8101** & 0.8936 & **287.0105** & **11.6790** & **17.7721** \\ \(7\) & SVR & 0.8041 & 0.8880 & 365.4109 & 13.7256 & 21.9900 \\ \(7\) & SOM-SVR & **0.8120** & 0.8917 & 359.7340 & 13.5181 & 21.3260 \\ \(7\) & SARIMA-SVR & 0.7969 & 0.8872 & 306.1086 & 12.0327 & 19.7383 \\ \(7\) & **SOM-SARIMA-SVR** & 0.8101 & **0.8927** & **289.7224** & **11.8295** & **17.9783** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the best mean prediction performance results of the single models (SVR), the combined models (SOM-SVR), the hybrid model (SARIMA-SVR) and the proposed model (SOM-SARIMA-SVR) for one-day and seven-day prediction horizon. Best values in bold. Figure 6: Comparison of the observed and predicted value with the most accurate models. \(ph=1\) case. the combination of models and the hybridization of them. In this study, a combined-hybrid SOM-SARIMA-SVR forecasting model has been proposed based on a three-step procedure to predict the daily number of containers passing through a Border Inspection Post of a maritime port. To reduce the complexity of the problem, a clustering SOM is first applied to obtain smaller regions with similar statistical features which may be easier to predict. A SARIMA model is then fitted within each cluster to obtain predicted values and residuals of the clustered database. Finally, a SVR model is used to forecast each cluster independently using the variables obtained from the second step together with the original data as inputs. The combination of each cluster results in the whole predicted time series. The above methodology involves the advantages of combining a forecasting model with a clustering technique and the strengths of the hybrid models in capture linear and nonlinear patterns. The proposed SOM-SARIMA-SVR model has been developed and compared to other possible methodologies implied in the process (SVR, SOM-SVR and SARIMA-SVR). The results showed that the SOM-SARIMA-SVR model was the most competitive model, improving the forecasting performance of the rest of the models concerning the prediction of the container demand, outperforming these methodologies. Particularly, considering the SOM-SARIMA-SVR model, two hybrid approaches were assessed: the classical additive approach, where the error term (\(e\)) of the linear model is the input of the nonlinear model; and the proposed approach, where the prediction is a function of the original data (\(y\)) and the error term (\(e\)), and the prediction of the linear model (\(p\)). Most accurate results were yielded by the second approach in all cases tested. In addition, there are no significant differences between the prediction performance using both prediction horizons. The same occurs with the introduction of certain variables as inputs. These outcomes highlight the robustness of the model. This investigation suggests thereby that the proposed hybrid approach achieves better outcomes getting higher forecasting performance than the classical additive hybrid approach. To conclude, this study is the first one in using the SOM-SARIMA-SVR model to forecast the volume of containers passing through a BIP of ports in particular, and for time series forecasting in general with promising results.