## 5 Conclusions  
This paper proposes a novel model for long-term spatial-temporal prediction called multi-scale spatial-temporal transformer network that is based on an improved STTNs. Introducing the GWNN and autoformer, MSSTTN models spatial-temporal dependencies in a multi-scale manner. We enable the scaling parameter to be learnable to pass the graph signals and construct a trend-cyclical part extraction method in a multi-scale manner to enhance the time series analysis. Otherwise, the series decomposition and Auto-Correlation mechanism in autoformer endow MSSTTN with powerful time series analysis ability. Based on series decomposition, this paper proposes a multi-scale decomposition method using windows of various scales to enhance the time series analysis ability. Experiments on three real-world datasets demonstrate that MSSTTN is superior in long-term spatial-temporal prediction.  
Nevertheless, the complexity of autoformer gives MSSTTN a relatively high complexity, and graph wavelets must be recomputed during scaling the parameter learning. These result in certain computations. In future work, how to reduce the model complexity and simplify the recomputing of the graph wavelets while maintaining the prediction effect is a problem worth studying.  
Conceptualization, D.Z.; Methodology, J.M.; Writing--original draft, J.M.; Writing--review & editing, J.M., D.Z. and W.H.; Visualization, J.M.; Supervision, D.Z. and [PERSON]; Funding acquisition, [PERSON] All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Key projects supported by the NSFC joint fund under grant U1911205, in part by the science and technology project of Hubei Provincial Department of Natural Resources under grant ZRZY2023 KJ15.  
**Data Availability Statement**: In this paper, we evaluate our model on three widely used traffic prediction open datasets, namely PEMS03, PEMS04, and PEMS08 which are obtained from [11].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Hyperparameter** & **Setting** & **MAE/MAPE (\%)/RMSE** \\ \hline \multirow{2}{*}{Encoder layers} & 1 & 20.05/14.29/32.39 \\  & 2 & 20.13/14.25/32.53 \\ \hline \multirow{2}{*}{Decoder layers} & 1 & 20.31/14.45/32.64 \\  & 2 & 20.05/14.29/32.39 \\  & 3 & 20.11/14.27/32.46 \\ \hline \multirow{2}{*}{Blocks} & 1 & 23.12/15.64/36.08 \\  & 2 & 21.89/14.96/34.21 \\ \cline{1-1}  & 3 & 20.05/14.29/32.39 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Hyperparameter tuning.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **MAE** & **MAPE (\%)** & **RMSE** \\ \hline GraphWaveNet & 24.18/25.45/28.04 & **9.30**/9.86/10.71 & **36.21**/38.15/41.30 \\ STTNs & 24.10/25.34/27.73 & 9.62/10.02/10.87 & 36.33/38.07/41.00 \\ ASTGNN & **23.98**/25.64/28.21 & 9.38/10.04/11.14 & **36.21**/38.43/41.61 \\ FOGS & 24.15/25.72/28.12 & 9.39/9.96/10.97 & 36.36/38.48/41.53 \\ MSSTTN & 24.28/**24.77**/**26.02** & 9.65/**9.85**/**10.35** & 36.67/**37.52**/**39.16** \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of PEMS04 prediction results on rush hours.  
**Acknowledgments:** We would like to express our appreciation to [PERSON] and [PERSON] from the Information Center, Department of Natural Resources of Hubei Province, Wuhan, for their contributions to this paper.  
**Conflicts of Interest:** The authors declare no conflict of interest.