# Container Volume Prediction Using Time-Series Decomposition with a Long Short-Term Memory Models
## 4 Experiments and Results  
The computing environment was Windows 10 run on an RTX 2070 SUPER GPU and Python 3.7. The neural network models were configured using the Keras framework. Data from the Busan Port Authority's shipping and port logistics analysis system were used to evaluate the effectiveness of the Busan Port loading container volume forecast proposed in this study. The loading container consists of import, export, and transfer; the container volume is aggregated based on monthly indicators. In this study, import, export, and transfer containers were combined to obtain the total loaded container volume  
The original container volume data is stored monthly starting from March 2003 and extending to October 2020. External variables have the same time range as the container volume data. The train and test data are approximately split into 80% (March 2003-April 2018) and 20% (May 2018-October 2020), respectively. External variables follow the same split proportional rate as the container volume data. All variables are numerical data, and the summary is shown in Table 3.  
When each time-series element is predicted in combination with an external variable as a multivariate model, the optimal layer exploration is initiated according to each element. The loss function used in the predictions was RMSE; moreover, an Adam optimizer was used. The optimizer instigates the search process for the value of hyperparameters such that the value of the loss function is minimized owing to the learning of neural network models. In this study, the optimal value is computed using an Adam optimizer by considering the direction of inertia after each calculation and previous situations together at every step. The trend and residual have different model layers and the model configuration is shown in Table 4.  
Figure 8 shows a comparison between the actual and predicted values for six months from May to October 2020. In the figure, trend prediction reasonably follows the actual trend except in the last month. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Container Volume** & **MPI** & **IPI** & **Import-Export Weight** & **CPI** & **Import-Export Price** \\ \hline Count & 212 & 212 & 212 & 212 & 212 & 212 \\ Mean & 1,113,716 & 89 & 91 & 93 & 84,078 & 72,457,330 \\ Standard Deviation & 279,131 & 16 & 13 & 9 & 13,084 & 19,434,553 \\ Minimum & 628,653 & 533 & 64 & 75 & 55,322 & 28,189,734 \\
25\% & 838,584 & 75 & 81 & 84 & 71,439 & 56,477,292 \\
50\% & 1,129,280 & 96 & 94 & 97 & 86,925 & 77,572,986 \\
75\% & 1,353,759 & 105 & 102 & 101 & 93,748 & 89,170,656 \\ Maximum & 1,632,064 & 114 & 121 & 106 & 108,726 & 103,340,928 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary statistics of the variables. For seasonality prediction, an accuracy of approximately 99% was recorded owing to the characteristic of representing the iteration of the same value based on the fourth quarter. Thus, we have a pattern of four values (-3320, \(-\)31,812, 25,311, and 9822) repeating continuously. Finally, the residuals were predicted by combining the residuals of the external variables. As mentioned in Section 3.3, external variables should also be decomposed before inputting into the model. Table 5 is an example of a combination of residuals in a loaded container volume and those in external variables. Since residual components can provide negative values, which can affect the model, so all external variables are also represented in decomposed components.