# Container Volume Prediction Using Time-Series Decomposition with a Long Short-Term Memory Models
## 2 Background
### Related Works  
Time-series data observations are chronologically ordered and are used to predict current and future movements based on historical data records. Thus, time-series data consist of trend, seasonality, and residual information; the sum or product of these components can influence time-series data. The use of additive or multiplicative models, formulated from the sum or product of the components, usually depends on the size of the seasonal pattern that is obtained by separating the effects of individual factors of the time-series components. If the size of the seasonal pattern does not significantly affect the size of the data, then an additive model is formulated; however, if the size of the seasonal pattern significantly affects the size of the data, then a multiplicative model is formulated [7]. Equations (1) and (2) represent the additive and multiplicative models of time series data, respectively.  
\[\text{Addictive model}\ Y_{t}=\text{{Trend}}_{t}+\text{{Seasonality}}_{t}+ \text{{Residual}}_{t} \tag{1}\]  
\[\text{Multiplicative model}\ Y_{t}=\text{{Trend}}_{t}\times\text{{Seasonality}}_{t} \times\text{{Residual}}_{t} \tag{2}\]  
Among the many time-series methodologies used for container volume prediction, the SARIMA method is extensively implemented. SARIMA is an extension of the existing ARIMA models to facilitate the direct modeling of seasonal elements of time-series data [8]. In a study on container volume estimation and prediction, which was limited to the largest port in Korea, [PERSON] [9] estimated future forecasts of container volume based on the periodicity and seasonality of Busan port in Korea. The traditional time-series models implemented in previous studies utilizing only volume data are not capable of reflecting estimates of variability in container volume. Therefore, the focus is on the development of models that can flexibly accept variability in container volume. [PERSON] et al. [5] highlight the advantages of including beggar economic indicators such as GDP per capita, purchasing power parity, import price, export price, and the unemployment rate for improving economic and analytical performances of models; they apply the gross domestic product, purchasing power, import, and export rates as external variables for predicting container volume at Koper ports. In this study, macroeconomic indicators are applied to the ARIMA model to obtain more accurate volume prediction results. The prediction of container volume using the external variables provided more sensitive results. This emphasized that the prediction of container volume using economic indicators is essential.  
The application of various external variables to the prediction model to compensate for the threshold improves the model performance but presents a new problem of the need to study the overall trend (upward, steady, or downward) of the container volume [6]. Preemptive directions can be presented based on the estimates in one-year terms; however, the need to obtain preemptive directions at detailed stages emphasized the necessity of improving the performance of container volume prediction techniques followed by various studies using deep learning [6].