# Multiscale Backcast Convolution Neural Network for Traffic Flow Prediction in The Frequency Domain
## 1 Introduction  
Recent economic developments worldwide have led to a steady increase in road traffic. Because many of the problems posed by the increase of traffic flow are difficult to solve, such as traffic jams, traffic accident and so on [1, 2, 3], intelligent transportation systems (ITS) have become increasingly important [4]. Current technology can maximize road utilization without changing the existing road structure, and various scheduling algorithms rely on traffic flow data, which can be accessed through various data mining algorithms. Traffic flow and calendar time are strongly coupled because traffic flow varies over different time periods, and can be treated as a natural time series. In addition, because traffic intersections are key nodes for analyzing traffic flow and different intersections are strongly coupled over space, traffic flow data are also characterized by spatial correlations. In summary, traffic flow data represent a form of spatially correlated time series data, and the prediction of traffic flow time series can guide the deployment of downstream processing algorithms. In the last twenty years, a lot of traffic flow prediction approaches were proposed from different perspectives [5, 6, 7, 8]. The traffic flow data is represented by time series data; hence, the most typical approaches used for traffic flow prediction are AutoRegressive based approaches [9, 10, 11]. The AutoRegressive based methods suppose that the prediction time stamp result is a linear combination of the past several time stamp values. This priori hypotheses works well in solving some simple prediction tasks but brings new problems at the same time, such as ignoring spatial correlation between multiple time series, unable tocapture complex temporal varying mode, etc. Similarly, Support Vector Regression based approaches [12; 13], another classical approach, faces a homologous problem. The accuracy of these classical approaches is relatively low due to the limited fitting and generalization ability of functions, especially for solving prediction tasks with a modern complex traffic flow time series dataset. As the deep learning techniques develop, the fitting and generalization ability of learning system is greatly raised. In recent years, the methods used for traffic flow prediction have been mainly based on deep learning techniques operating over temporal and spatial dimensions, such as Feed-forward Neural Networks [14], Recurrent Neural Networks (RNN) [15], and Convolutional Neural Networks (CNN) [16]. After intense research and development, these networks have achieved good results in traffic flow prediction problems, as recently demonstrated by Bi-LSTM [17], StemGNN [18], and Autoformer [19]. These findings go far beyond traditional statistical methods, which are essentially focused on the time-domain patterns of sequences and attempt to predict future information from past point-in-time information. Notwithstanding the success of machine learning in this area, two main problems remain unresolved. First, traffic flow data are strongly cyclical (traffic flow is more intense than usual during the morning and evening rush hours, and less intense on weekends than on weekdays). This important feature is difficult to model directly via a time-domain representation. Second, RNN architectures based on time-domain information are greatly affected by the length of the input sequence (as the length increases, model performance decreases and inference time increases). To overcome these limitations, in this study, we eliminate the influence of time domain characteristics by operating our analysis in the frequency domain, and we propose a multiscale convolutional feedback network that is also based on the frequency domain. The core contributions of this article are the following:  
1. This paper proposes a new prediction network based on a deep learning approach, which captures and learns the strong periodic pattern of traffic flow data by processing the frequency domain characteristics of traffic flow data.