# Deep Learning Forecasting for Supporting Terminal Operators in Port Business Development
## 4 Results
\begin{table}
\begin{tabular}{l l r r r r} \hline \hline  & **Type** & **SARIMA** & **CONV** & **LSTM** & **GRU** \\ \hline \multirow{8}{*}{2019 Forecasts} & empty & 14.97\% & 19.94\% & 9.51\% & 11.83\% \\  & full loaded domestic & 7.43\% & 8.62\% & 11.27\% & 13.37\% \\  & full loaded foreign & 6.96\% & 8.00\% & 8.19\% & 11.34\% \\  & full transit & 23.48\% & 9.10\% & 10.14\% & 9.05\% \\  & full unloaded domestic & 14.86\% & 42.85\% & 11.99\% & 9.83\% \\  & full unloaded foreign & 7.56\% & 7.27\% & 6.27\% & 5.49\% \\  & on aggregate & 12.54\% & 15.96\% & 9.56\% & 10.15\% \\ \hline \multirow{8}{*}{2020 Forecasts} & empty & 29.75\% & 19.51\% & 22.09\% & 21.13\% \\  & full loaded domestic & 20.28\% & 14.48\% & 19.60\% & 19.55\% \\ \cline{1-1}  & full loaded foreign & 10.84\% & 10.58\% & 8.72\% & 9.43\% \\ \cline{1-1}  & full transit & 19.08\% & 23.45\% & 28.42\% & 25.85\% \\ \cline{1-1}  & full unloaded domestic & 12.39\% & 43.13\% & 9.36\% & 7.79\% \\ \cline{1-1}  & full unloaded foreign & 13.10\% & 11.79\% & 14.46\% & 13.09\% \\ \cline{1-1}  & on aggregate & 17.57\% & 20.49\% & 17.11\% & 16.14\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Forecasting MAPE results for SARIMA, CONV, LSTM, and GRU models in 2019 and 2020. Figure 6: Performance of the SARIMA and GRU models expressed as MAPE for forecasting years 2019 (lighter) and 2020 (darker). Figure 7: Time series predictions of GRU and SARIMA models. We conclude this paragraph by analysing the representation of the seasonal components learned by the network during the training process. We focus on the GRU model in this part. The embedding layer, as described in Section 3.2, mapped the elements of the set \(\mathcal{S}\) (the months of the year) in a \(q_{s}=5\)-dimensional space, in which they were represented in an optimal way with respect to the outcome variable. The Euclidean distance of the levels in the new space is a measure of their similarity with respect to the target variable. In our case, the distance measured the similarity of the months to the container traffic volume. Since the visualisation of a month embedded in a five-dimensional space was complex, we performed principal component analysis (PCA) on the embedding features to reduce the dimensionality of the data with a minimum loss of information. In particular, we extracted the first two (of five) components, and the months were mapped into a new two-dimensional space \(\mathbb{R}^{5}\mapsto\mathbb{R}^{2}\). In our numerical experiments, the first two principal components explained about 95% of the total variability and represented the months of the year in a new bivariate space that allowed a simple graphical representation. Figure 9 plots the months of the year in this reduced-size space. We observed that the months characterised by similar (average) temperatures tended to be close to each other in the new space. In particular, the warm weather months (in red) were concentrated at the new space's bottom, while the cold weather months (in blue) were located in the remaining part of the new space. This suggests that the network recognises similar patterns in data referring to times of the year characterised by a similar climate and assigned similar weights to months with similar characteristics. Figure 8: Standardised residuals of the SARIMA and GRU models for the different months. Figure 9: Graphical representation of the months embedding \(z_{s}(s)\in\mathcal{R}^{5}\) after the dimensionality reduction (from 5 to 2) via principal component analysis.