## 1 Introduction  
The rise of intelligent transportation systems (ITSs) [1] has led to the increased importance of traffic prediction in urban management [2; 3; 4; 5]. As a core component of the aforementioned traffic applications, traffic prediction, which is a classical spatial-temporal prediction, has attracted the attention of many researchers. Spatial-temporal prediction mines future trends through learning historical data in time and space. Improving the accuracy of spatial-temporal prediction, especially long-term prediction, is of great significance. However, the intricate spatial-temporal dependencies pose a significant obstacle to achieving accurate spatial-temporal series prediction.  
Early mathematical spatial-temporal prediction models make predictions based on statistical methods [6; 7; 8] failed to deal with the dynamic correlations among variable parts in both the spatial and temporal dimensions. To address the weakness of statistical prediction methods, traditional shallow machine learning methods [9; 10] emphasize the linear mapping relation that can better capture the complex inherent laws in spatial-temporal data. However, they ignore the sequence connections that perform poorly in both spatial and temporal dependencies extraction. In contrast, deep learning methods perform better in complex spatial-temporal correlation capturing.  
Most existing spatial-temporal deep learning models cannot capture the fixed spatial dependencies in neighborhoods with an appropriate size and ignore multi-scale important temporal attributes, leading to a failure to match the accurate spatial correlations.  
To overcome the limitations, we propose the multi-scale spatial-temporal transformer network (MSSTTN) to extract information of various scales to improve spatial-temporal prediction. First, we introduce and improve the GWNN to capture multi-scale fixed spatial dependencies using different scaling parameters. Second, series decomposition and an Auto-Correlation mechanism are introduced to analyze the historical temporal patterns. Moreover, we propose to decompose the time series into different local trends, which facilitates the acquisition of temporal information at multiple scales and augments the precision of capturing temporal dependencies. The contributions of the paper are summarized as follows:  
* We introduced and improved the GWNN to the spatial-temporal transformer network. By making the scaling parameter learnable, the improved GWNN can aggregate the spatial features adaptively that strengthens the fixed spatial dependencies extraction.
* We proposed a novel series multi-scale decomposition to enhance time series analysis by trend-cyclical parts at various scales, making MSSTTN powerful in capturing long-term dependencies.
* We conducted experiments on three datasets, PEMS03, PEMS04, and PEMS08 [11], and the results demonstrate the superiority of MSSTTN in long-term spatial-temporal prediction.  
In the rest of this paper, Section 2 discusses the related work of spatial-temporal prediction. The architecture of MSSTTN is constructed in Section 3. Section 4 describes the experimental settings, conducts a series of experiments, and analyzes the results. Finally, the conclusions are discussed in Section 5.