# Deep Learning Forecasting for Supporting Terminal Operators in Port Business Development
## 4 Results
Table 3 compares the results of the SARIMA models against the LSTM, CONV, and GRU models with tanh activation in both forecasting scenarios. For the deep learning models, we considered the ensemble prediction, obtained as the average of the forecasts in 10 different runs. The MAPEs obtained by the different methods were reported at the single time series level and at the aggregate level, where all values were summed. First, we observed that the errors increased dramatically when moving from the 2019 forecasting scenario to the 2020 forecasts. This is quite reasonable, since container traffic volume showed a highly irregular pattern over the last year due to the COVID-19 outbreak. In addition, it is visible that the LSTM and GRU methods produced a lower global MAPE  
Figure 5: Forecasting MAPEbox plots for CONV, GRU, and LSTM. than the SARIMA models in both forecasting scenarios. On the contrary, the CONV model had poorer performances. This probably suggests that the evolution of container traffic can be better modelled by using recurrent neural network architectures than convolutional ones. Considering both scenarios, the GRU model appeared to be the best model. A further comparison between the performances of the GRU and SARIMA models is depicted in Figure 6 using barplots. Looking at the performance on individual series, in the 2019 forecasts, we observed that the improvement induced by the GRU models was especially large for the \"full transit\" and \"empty\" container volumes, which were two of the largest series in terms of size. In particular, the training of the deep learning models was carried out simultaneously on all data and pursued the minimisation of the global MAE in the training set. In this setting, it is not surprising that the learning algorithm put more weight on the larger series, which could produce larger residues, than the smaller ones. At the same time, the SARIMA approach appeared to be highly competitive on both \"full loaded\" series. The comparison between the forecasts obtained by the GRU and SARIMA models in this forecasting scenario is also graphically represented in Figure 7. In the 2020 forecasts, the GRU and LSTM models still overperformed the SARIMA model at the overall level, but the improvement appeared to be smaller. In this scenario, the only case in which the SARIMA approach yielded a lower MAPE than the GRU was the \"full transit\" container traffic volume. This evidence is in contrast with that observed in the first forecasting scenario. However, when analysing in greater detail the behaviour of the \"full transit\" container volume traffic, we observed that this series presented a large downward peak in the initial months of 2020 and a rebound in the summer months of 2020. All of the models investigated failed to predict the evolution of the \"full transit\" series, and this is not surprising given that these troughs were probably due to the COVID-19 outbreak. The reasons why the effects of the pandemic on the predictive ability of models were large in this particular series have yet to be clarified, and we plan to shed some light on this theme in a forthcoming work. Figure 8 shows the standardised residuals obtained by the SARIMA and GRU model, distinguished by month for all the time-series data. We observed that both models presented positive and negative residuals in all months. This evidence suggests that the SARIMA and the GRU model did not have a systematic error component. Furthermore, we note that the amplitude of the errors was generally stable over the different months.