## 1 Introduction
### Multimethodological Approach and Gaps  
The forecasting of container throughput is a typical time series forecasting problem. Changes in a time series are not only influenced by their own historical values, but also closely related to external factors [6]. However, most of the existing studies have focused on the unidimensional correlation between a port's hinterland economy and the container throughput, and lack a systematic consideration of the synergistic mechanism of multiple factors. But, a reasonable selection of the indicator data can effectively improve the predictive effect of the model [7]. Based on this, how to select suitable index data is one of the problems to be solved. And reasonable data processing is conducive to the improvement of the prediction accuracy of the model. Therefore, after obtaining the indicators, data enhancement methods should be used to improve the data quality.  
In the past decade or so, many scholars at home and abroad have tried to use traditional statistical models [8; 9], machine learning models [10; 11; 12; 13], and combined models [14; 15; 16; 17] for regression prediction and have achieved fruitful research results. However, statistical models only model linear relationships and are insensitive to nonlinear trends. And they rely on smoothness assumptions and require manual adjustment of the difference and seasonal cycle parameters. Therefore, in recent years, researchers have focused their  
Figure 1: The growth of number of containers and combined rail mileage. (**a**) Container throughput quantity and growth rate and (**b**) rail and road mileage and growth rate.  
attention on ML and DL models. For example, [PERSON] [18] used various machine learning methods to predict the CO\({}_{2}\) emissions from intermodal transport and to optimize transport planning. [PERSON] [19] used four deep learning architectures for recognizing the order status in complex supply chains. It was found that deep learning prediction models work better than machine learning prediction models. [PERSON] [20] used a CNN prediction model and two common machine learning prediction models to predict highway-railway-level crossing accidents, and compared their prediction performances. It was found that the CNN prediction model had a better prediction performance. However, in time series forecasting problems, researchers have focused their goals on traditional forecasting models, and less research has been conducted on deep learning models. Based on this, how to apply deep learning-related models to container throughput forecasting problems is what we need to consider.  
In summary, the current research gap can be summarized in two parts. The first is data selection and processing, and the second is the selection of the prediction models. Regarding the data selection and processing, single data decomposition is commonly used for regression prediction. On the contrary, this article uses processing methods, such as multi-index data upsampling and weight assignment. In terms of model selection, unlike previous studies that have used statistical models to predict container throughput, this paper applies a CNN model to time series prediction problems through multi-index time series data.