# Deep Learning Forecasting for Supporting Terminal Operators in Port Business Development
## 3 Materials and Methods
### Data  
In order to validate the effectiveness of the proposed methodology, we carried out some experiments on data downloaded from the website of the port of Barcelona. These data were also used in [39]. This port is one of the most important maritime logistics ports in the Mediterranean, with a land area of 10.653 square kilometers. Barcelona is the third largest port for container activity in Spain (after Valencia and Algeciras) and ninth in Europe. The port is managed by the Barcelona Port Authority. As one of the main ports in Spain--where it adopted the landlord governance model [16]--the Port of Barcelona is coordinated by Ports of the State, a state-owned organisation responsible for the meta-management of the 28 main Spanish port authorities that are in national seaports of general interest. In the port of Barcelona, there are two terminal operators specialised in container handling: \"APM Terminals Barcelona\" and \"BEST--Barcelona Europe South Terminal\". Both these container operators manage international terminals--linked with rail facilities--with more than 3000 m of berthing line and 17 container cranes.  
The website of the Port of Barcelona provides multivariate time series data related to container traffic. The dataset includes monthly observations from January 2010 to December 2020 (\(|\mathcal{S}|=12\), \(|\mathcal{Y}|=11\), and \(\mathcal{T}=\{t\in\mathbb{N}:t\leq 132\}\)) related to the count of containers, which are broken down into six categories: loaded and unloaded foreign, loaded and unloaded domestic, empty, and transit. A separate analysis of the different categories is also especially interesting in light of the reshaping of global supply chains, with a thrust toward regionalisation that is being amplified by attempts to build resilience in response to the COVID-19 outbreak.  
First, explanatory data analysis was carried out. Table 1 reports some statistics (mean, coefficient of variation (CoV), and range) of our dataset. We observe that the time series under analysis presented very different magnitudes. For example, the volume of full unloaded domestic containers was the smallest, while the volume of containers in transit was the largest.  
Figure 3 provides pairwise scatter plots (below the main diagonal) and Pearson correlation coefficients (above the main diagonal) among the time series of interest, arranged in matrix form. From both, we noted moderate positive correlations. The 3 stars next to the correlation coefficients indicate that the corresponding p-values were less than 0.001. This evidence suggests that a multivariate model could exploit the information among the different series and produce more accurate predictions.  
Figure 4 shows the box plots for the different container types grouped by month. The red boxes refer to the warm months, while the blue ones represent the cold months.  
\begin{table}
\begin{tabular}{l r r r r r} \hline \hline
**Type** & **Mean** & **CoV** & **Min** & **Max** & **Range** \\ \hline empty & 48.3668 & 0.2611 & 27.5010 & 86.2680 & 58.7670 \\ full loaded domestic & 7.5032 & 0.1888 & 3.7720 & 10.4460 & 6.6740 \\ full loaded foreign & 52.8784 & 0.1842 & 26.3830 & 71.5410 & 45.1580 \\ full transit & 47.7746 & 0.6771 & 14.0320 & 126.9690 & 112.9370 \\ full unloaded domestic & 1.7183 & 0.2168 & 1.0070 & 2.8020 & 1.7950 \\ full unloaded foreign & 40.4105 & 0.1722 & 26.4280 & 56.8010 & 30.3730 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Data statistics.  
Figure 2: A graphical diagram of the proposed neural network model.  
Some common elements can be observed among the different series. First, we observed that container traffic increased in the warm weather months, but this effect was more pronounced in some series and less so in others.  
Figure 3: Pairwise scatter plots of the container traffic volume data. Correlation coefficients are marked with *** if the \(p\)-value of them being zero is less than 0.001.