# Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network
## 5 Conclusions  
Multivariate time series have complex spatiotemporal information, and there are dependencies among multiple series. In addition, the time series has a periodic pattern. According to the characteristics of multivariate time series, a multivariate time series deep spatiotemporal forecasting model with a graph neural network (MDST-GNN) is proposed in this paper. It comprises four modules: graph learning, temporal convolution, graph convolution, and down-sampling convolution. In order to deal with complex information better, the model adopts a graph neural network to transform complex information into processable graph information. Furthermore, the model utilizes a temporal convolutional network to extract temporal information in the predicted sequence. Graph convolutional networks are used to extract spatiotemporal information of predicted sequences. The attention method is added to improve the information filtering ability. Down-sampling convolutional networks are used to extract deep spatiotemporal information. The MDST-GNN model can filter out irrelevant dependency information between graph nodes and is more suitable for multivariate time series forecasting. The prediction accuracy of data peaks can be enhanced by capturing deep spatiotemporal information. In experiments, the proposed model predicts future values at different intervals for four datasets. Based on the above discussion and experimental results, the advantages of MDST-GNN are verified in the experimental results on four sets of public datasets, and the attention method and down-sampling convolutional network proposed in this paper improve the prediction accuracy of the model.  
The MDST-GNN model has achieved significant improvements on multiple datasets, but there are still certain problems in predicting data with large short-term fluctuations  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Metrics** & **w/o A** & **w/o S** & **MDST-GNN** \\ \hline \multirow{2}{*}{Solar Energy} & RRMSE & 0.4279 & 0.429 & **0.4119** \\  & CORR & 0.903 & 0.9042 & **0.9103** \\ \hline \multirow{2}{*}{Traffic} & RRMSE & 0.4584 & 0.4577 & **0.4452** \\  & CORR & 0.8732 & 0.87 & **0.8792** \\ \hline \multirow{2}{*}{Electricity} & RRMSE & 0.0952 & 0.095 & **0.0922** \\  & CORR & 0.9212 & 0.9213 & **0.9222** \\ \hline \multirow{2}{*}{Exchange Rate} & RRMSE & 0.0444 & 0.0459 & **0.0431** \\  & CORR & 0.939 & 0.9344 & **0.9392** \\ \hline \hline \end{tabular} Note: The optimal results are in bold black.  
\end{table}
Table 4: Ablation study (Horizon = 24).  
Figure 13: Time series (one variable) predicted and true values for the Electricity test set (Horizon = 24). Left (**a**) is the w/o S model result, right (**b**) is the result of the full model.  
such as Solar Energy. This is mainly caused by the insensitivity of convolutional networks to local fluctuations and the lack of long-term memory information. At the same time, the model has many parameters, and how to reduce the model parameters while maintaining good prediction performance is a problem worth pondering. Our next research will revolve around the problem of model lightweight and insensitivity to local fluctuations.  
Conceptualization, Z.H., C.Z. and Y.H.; data curation, Z.H.; methodology, Z.H. and C.Z.; software, Z.H.; supervision, C.Z. and Y.H.; validation, Z.H.; writing--original draft, Z.H. and C.Z.; writing--review and editing, Z.H., C.Z. and Y.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Nos. 61862062, 61104035).  
Not applicable.  
The data presented in this study are openly available in Github ([[https://github.com/laiguokun/multivariate-time-series-data](https://github.com/laiguokun/multivariate-time-series-data)]([https://github.com/laiguokun/multivariate-time-series-data](https://github.com/laiguokun/multivariate-time-series-data)), accessed on 2 February 2022).  
The authors declare no conflict of interest.