# Container Volume Prediction Using Time-Series Decomposition with a Long Short-Term Memory Models
## 1 Introduction  
Deep learning is a type of machine learning in which the design of algorithms like artificial neural networks is inspired by the working of the human brain; additionally, the algorithms learn from large amounts of data [1]. Deep learning algorithm generally utilizes hidden layers that are learned through various combinations in deep neural networks. Hidden layers are all layers between the input layer and the output layer which compose the deep neural networks. This type of learning exhibits human-level performance in various fields, such as image recognition, text classification, and speech recognition. It is also useful as an analytical model for prediction in diverse disciplines, such as economy, medicine, and physics. As time-series data is widely represented in various fields, container volume data is one of the representative time series data in the port sector. Deep learning neural networks are capable of automatically learning complex mappings from inputs to outputs and support multiple inputs and outputs, thus demonstrating good performance in the long-term predictive performance of time-series data [1]. Thus, a time-series prediction model with deep learning can easily deal with multicollinearity or nonlinear problems that are not addressed by traditional statistical models [2]. In this study, we applied deep learning prediction models to container volume predictions, which are in a sense, representative time-series data, to yield better prediction results. Container volume data is representative continuous time-series data that have been actively studied by statistical models from researchers. Previous studies on container volume prediction have implemented models, such as autoregressive integrated moving average (ARIMA), seasonal autoregressive integrated moving average (SARIMA), and traditional regression. However, the limitation of traditional time-series prediction techniques is that the performance reduces when unexpected variations are reflected in the data [3]. Various external factors, such as the financial crisis and internal and external economic impacts reduce the stability of time-series data  
In particular, Busan Port, known as the largest port in Korea, has gained interest from many researchers in utilizing deep learning models with time-series prediction. The container volume prediction at Busan port in Korea, indicated that the development of the port is closely related to national competitiveness and in fact, strengthens it; hence, accurate prediction of container volume is essential [4]. In an effort to strengthen the Busan port in Korea, the study of predicting container volume at Busan Port has been expanded from statistical methodology to univariate prediction, and multivariate prediction by deep learning models. Deep learning is broadly used in container volume prediction analysis models, wherein univariate time-series data are combined with deep learning models [4]. Deep learning-based container volume prediction shows improved results over traditional statistical models. Not only a univariate prediction but also a combination of deep learning-based models with external variables improves flexibility and increases the model's variability acceptance from the data. A multivariate time-series prediction model that includes external variables is appropriate for more delicate container volume predictions. Combinations of external variables give an important glimpse of utilizing essential factors in deep learning that could be enriched in the prediction. Thus, in this study, we seek to explore and apply external variables that are relevant to the container volume predictions. The selection criteria are correlations and trends that have proven influence according to previous research works [5; 6]. We applied various external factors from the previous studies on the container volume prediction literature, then conduct each variable with the vector auto regressive (VAR) model.