## 4 Experimental Results and Discussion  
The results of the proposed hybrid SARIMA-SOM-SVR models to predict the daily number of containers passing through the BIP of the Port of Algeciras Bay are presented and discussed in this section. These results are those obtained in the third step of the proposed procedure and they were assessed and compared with those achieved with the single SVR, the combined SOM-SVR, and the hybrid SARIMA-SVR models. Nevertheless, a cursory discussion of the previous results obtained at the first and the second steps (SARIMA and SOM stages) is given in this section for a general overview. The prediction was one-step ahead and two prediction horizons were considered, \(ph=1\) and \(ph=7\) days. First, a two-dimensional competitive Kohonen network (SOM 2-D) was employed as a clustering technique. The final aim of this step is to divide the whole database into several disjoint clusters with similar statistical features. The assumption is that the prediction of a smaller cluster can be easier than the prediction of the whole database. Testing different configurations of the SOM network, the most appropriate SOM map size for the data was \(8\times 8\) neurons in the output layer with a hexagonal grid topology and a three-dimensional input space. Figure 3a represents the SOM weight positions, which shows the locations of the data points and the weight vectors after the SOM algorithm was trained. Grey and green points represent neurons and input vectors, respectively. Red lines are the connections between neurons. Although the figure suggests the existence of two different groups (a group appears in the bottom-left region and another more disperse group in the central region), not all the weights can be visualized at the same time (one weight for each element of the input vector). Thus, the SOM neighbor distances could be useful (Figure 3b). This figure indicates the distances between neighboring neurons, where grey hexagons represent the neurons (\(8\times 8\) map), connecting themselves by the red lines. The color of the segments containing these red lines indicates the distance between neighboring neurons. Lighter colors represent smaller distances, whereas larger distances are represented by darker colors. As the figure indicates, a group of light segments appear in the bottom-right region. This region is bounded by some dark segments. According with the previous figure, this situation indicates that the SOM network has clustered the data into two groups. These results can be contrasted analytically and are collected in Table 2, which shows the best results obtained per cluster and its input-vector configuration. Based on two clustering performance indexes (CQI\({}_{1}\), and CQI\({}_{2}\)), the two-classes clustering was confirmed to be the best choice for the time series, reaching the highest values of CQI\({}_{1}\) and CQI\({}_{2}\) (0.659 and 717.548, respectively). Consequently, the database was divided into two groups, hereinafter called Cluster 1 and Cluster 2. These results were achieved using a three-element input vector (\(nc=3\)) with a temporal leap of 7-day in the past. Therefore, the input vector \(x_{t}\) is comprised of the actual value of the time series \(y_{t}\), and two 7-day lagged past value (\(y_{t-7}\) and \(y_{t-14}\)), conforming a three-dimensional input space. That is, \(x_{t}=[y_{t},y_{t-7},y_{t-14}]^{T}\), where \(t=1,2,\ldots,1461\). Figure 3: (**a**) The SOM weight positions and (**b**) the SOM neighbor distances between neurons. A SARIMA model was applied independently in each cluster in the second step. Considering the nature of the time series of each cluster, the clustered data was stationarized in mean (using a logarithmic transformation) and variance (using second differencing for Cluster 1 and second seasonal differencing for Cluster 2). Then, using an iterative trial-and-error procedure, the best-fitted models were ARIMA(2,0,3) for Cluster 1 (without seasonal part) and SARIMA(2,1,2)(2,1,3)\({}_{5}\), with a seasonality of 5 days for Cluster 2.