# Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network
## 4 Experiment Analysis
### Results  
The experiments are carried based on four test sets for the validation of the MDST-GNN model. And the evaluation results of all methods are summarized in Table 3. The horizon is set to 3, 6, 12, and 24 to predict the value after a specified time period in the future. For example, it represents forecasting 3 to 24 h into the future for electricity and traffic values in the Traffic and Electricity datasets. In Solar Energy, it means forecasting solar energy values 30 to 240 min into the future. In Exchange Rate, it represents the forecasted exchange rate value for the next 3 to 24 days. When the value of Horizon is larger, the prediction task is more difficult. The optimal results for forecast are highlighted in the table \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Model Setting** & \multicolumn{3}{c}{**Solar Energy**} & \multicolumn{3}{c}{**Traffic**} & \multicolumn{3}{c}{**Electricity**} & \multicolumn{3}{c}{**Exchange Rate**} \\ \hline Horizon & 3 & 6 & 12 & 24 & 3 & 6 & 12 & 24 & 3 & 6 & 12 & 24 & 3 & 6 & 12 & 24 \\ \hline Batch size & \multicolumn{3}{c}{8} & \multicolumn{3}{c}{16} & \multicolumn{3}{c}{32} & \multicolumn{3}{c}{4} \\ \hline Learning rate & \multicolumn{3}{c}{\(1\times 10^{-4}\)} & \multicolumn{3}{c}{\(1\times 10^{-4}\)} & \multicolumn{3}{c}{\(1\times 10^{-3}\)} & \multicolumn{3}{c}{\(5\times 10^{-4}\)} \\ \hline Window length & \multicolumn{3}{c}{168} & \multicolumn{3}{c}{168} & \multicolumn{3}{c}{168} & \multicolumn{3}{c}{168} \\ \hline Layers & 4 & 4 & 4 & 4 & 4 & 4 \\ \hline Num nodes & 137 & 862 & 321 & 8 \\ \hline Weight decay & \multicolumn{3}{c}{\(1\times 10^{-4}\)} & \multicolumn{3}{c}{\(1\times 10^{-5}\)} & \multicolumn{3}{c}{\(1\times 10^{-4}\)} & \multicolumn{3}{c}{\(1\times 10^{-4}\)} \\ \hline Num layer & 4 & 3 & 3 & 3 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameter Settings. Figure 8: Number of neighbors and Layers parameter analysis in Exchange Rate. Left (**a**) is the RRMSE result of the parameter Number of neighbors taking 0, 2, 4, and 8 respectively, and right (**b**) is the RRMSE result of the parameter Layers from 0 to 6.  
in bold black, and the suboptimal results are shown in red. Finally, the comparison results between the MDST-GNN model and other related models are shown in Table 3.  
We plot the RRMSE results for all methods of Electricity and Traffic, as shown in Figure 9. From the figure, it can be found that the method using neural network significantly outperforms the VARMLP model in the dataset. Obviously, neural networks have more advantages in time series forecasting. Subsequent models using neural networks have improved their prediction accuracy. Among them, MTGNN combined with spatial information outperforms LSTNet and TAP-LSTM models in results. The SCINet model also has good results in some datasets. Figure 9 shows that the RRMSE of multiple models is relatively stable, and the prediction accuracy of each model is improved. At the same time, Figure 9 can see that the MTGNN model fluctuates when the horizon is 6, which indicates that the spatial dependence of the dataset is weak when the horizon is 6, which interferes with the model. Compared with MTGNN, the MDST-GNN model has smaller fluctuations in this part, which shows that the attention method plays a role in filtering information and reduces the interference of irrelevant information. When the horizon is other values, the RRMSE tends to be stable. The RRMSE metric of our model is improved by 1%, 1.4%, 3.5%, and 3.3% on the Electricity dataset compared to the state-of-the-art method. Furthermore, on the Traffic dataset, when the horizon is 12, the RRMSE metric is 1.9% higher than the best baseline method, which proves the effectiveness of the model. More importantly, forecasts have