## 4 Experimental Results and Discussion
It may be caused by the high number of model tested, approximately about \(10^{6}\) models for each prediction scheme, where there are parameter configurations almost equal. In this sense and in order to get the smallest MAE value (11.679), the best-fitted network of Cluster 1 for this hybrid configuration 2 in the third step is composed by autoregressive window sizes of twelve for the \(y\) input variable (\(ny=12\)) and two for the \(e\) input from SARIMA step (\(ne=2\)), being the optimal SVR parameters \(C=200\), \(\gamma=2^{-4}\) and \(\varepsilon=2^{-8}\). To model Cluster 2, the best parameter configuration was \(ny=12\), \(ne=2\), \(C=50\), \(\gamma=2^{-2}\) and \(\varepsilon=2^{-2}\). For this network architecture, the number and size of SVR inputs coincide in both clusters. The final prediction is reached joining the predicted values of the two clusters. The best network architecture of the hybrid approach 2 is plotted in Figure 5.  
To conclude, a complete comparison among other hybrid models proposed in literature was performed in order to gain a comprehensive view of the real improvement established by the proposed model. Then, the most accurate single SVR model, the most accurate combined SOM-SVR model and the most accurate hybrid SARIMA-SVR model were also compared against the most accurate proposed model. These comparisons are summarized in Table 4, where values and models in bold indicate  
Figure 5: Best-fitting SVR network architecture for each cluster of SOM-SARIMA-SVR-2 hybrid model in the third step (\(ph=1\) case). \(C\), \(\gamma\) and \(\varepsilon\) are the SVR parameters. Only the inputs \(y\) and \(e\) are used. the best overall performance index and model, respectively, considering both prediction horizons. As Table 4 shows, the proposed SOM-SARIMA-SVR model outperforms the rest of the models in both prediction horizons. The SOM-SARIMA-SVR model is more competitive than the other models in four of the five performance indexes. Interestingly, another model achieves the highest value in one of the five performance index (SARIMA-SVR for \(d\) and \(ph=1\); SOM-SVR for R and \(ph=7\)). It can be concluded that the proposed model performs significantly better than the rest of models, especially in terms of MSE, MAE and MAPE values. This suggest that the \"divide-and-conquer\" principle, introduced with the usage of the clustering stage, can improve the performance of the hybrid models that consider the hybridization of linear and nonlinear forecasting techniques. The proposed methodology combines the strengths of the combined forecasting models with a clustering stage (clustering + forecasting technique) with the advantages of hybrid forecasting models (linear + nonlinear forecasting technique). The combined-hybrid approach has proved to be more effective than the other models in forecasting tasks and particularly in predicting the daily number of containers to be inspected at BIPs in ports and overcomes SOM-SVR model. Figure 6 represents a comparison point-to-point between the observed and predicted values for the best-fitted models concerning the \(ph=1\) (at the top) and \(ph=7\) case (at the bottom), respectively. An example period of five weeks of the year 2012 is represented. These figures clearly show that the proposed model produces a better fit to the data. The SARIMA-SOM-SVR model provides a better prediction of the daily number of containers passing through the BIP even in cases where the values are more difficult to predict.