# Container Volume Prediction Using Time-Series Decomposition with a Long Short-Term Memory Models
## 3 Method
### Data Analysis  
The container data are time-series data composed of three elements: trend, seasonality, and residual information. Time-series data represent a set of sequentially determined datasets collected over a period. That is, time-series data indicate that data exist over a period of time. They usually depend on historical series up to a point in time when  
Figure 4: Flowchart of proposed method.  
observed. This indicates that time-series data-based predictions analyze the observed historical data and apply the corresponding time-series prediction models [13]. In this study, we first conducted time-series decomposition to explore the features of the volume data. Volume data are characterized by additive models; the core components consist of trends, seasonality, and residuals. The following tables and figures illustrate the components of the time-series decomposition of container volume data. Each component of the container volume is listed in Table 1.  
When time-series data consist of deterministic components proportional to the period, they are said to have trends. Trends in time-series data also affect testing and modeling. This is because the reliability of time-series models is relevant in properly identifying and processing trends over time.  
Seasonality is characterized when time-series data show regular and predictable patterns according to the time period from the data. This characteristic of time-series data helps to improve the performance of modeling because the relationship between input and output variables improves when seasonal components of time-series data are identified and removed. In addition, seasonal definitions of time-series provide new information to improve the model performance.  
Finally, the residuals represent the remaining components after trend and seasonality characteristics resulting from fluctuations in the time-series are removed from the time-series data. Residuals have no correlation; however, if a correlation exists, then the remaining information should be used in the prediction calculation. Furthermore, the mean of the residuals is zero. If the mean has a nonzero value, the prediction is prone to error.  
The historical records of loading container volume data at Busan Port that represent the volume figures and trends for 2017-2018 and 2019-2020 are different. Figure 5 represents a comparison of container volumes and trends for the years 2017-2018.  
It can be observed that the gap between each line is negligible, and the trend is shown to some extent. Based on the time-series decomposition characteristics, we know that there is no significant variation in the value of the residuals among the time-series elements of the container volume. For seasonality, the same value is repeated based on the fourth quarter; hence, the deviation of the trend from the value of the container volume exhibits low error indicating that the value of the residual does not deviate significantly.  
However, the container volume data and trends for the years 2019-2020 shown in Figure 6 indicate a different pattern from that shown in Figure 5 for the previous two years. Data from the volume itself indicate a sharp increase compared to the last two years; however, the trend over the past two years tends to be more modest. That is, the variation in the residuals of the volume increases with time. The residual standard deviation for 2017-2018 is 191.4 whereas that for 2019-2020 is 222.3. The inherent variability in container volume data increases with an increase in time. Furthermore, container volume data are  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Components** & **Graphs** \\ \hline Trend & 1,000,000 \\ Seasonality & -1,000,000 \\ Residual & 2004 206 2008 2012 2014 2016 2018 2020 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Container volume components visualization.  
particularly vulnerable to complexity and variability due to internal and external economic and environmental changes; hence, single variables alone have limitations in prediction performance.