# Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network
## 4 Experiment Analysis
### Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Dataset**}} & \multicolumn{6}{c}{**Solar Energy**} & \multicolumn{6}{c}{**Traffic**} & \multicolumn{6}{c}{**Electricity**} & \multicolumn{6}{c}{**Exchange Rate**} \\ \cline{2-19}  & \multicolumn{4}{c}{**Horizon**} & \multicolumn{4}{c}{**Horizon**} & \multicolumn{4}{c}{**Horizon**} & \multicolumn{4}{c}{**Horizon**} & \multicolumn{4}{c}{**Horizon**} \\ \hline Methods & Metrics & 3 & 6 & 12 & 24 & 3 & 6 & 12 & 24 & 3 & 6 & 12 & 24 & 3 & 6 & 12 & 24 \\ \hline \multirow{2}{*}{VARMLP} & RRMSE & 0.1922 & 0.2679 & 0.4244 & 0.6841 & 0.5582 & 0.6579 & 0.6203 & 0.6146 & 0.1393 & 0.162 & 0.1557 & 0.1274 & 0.0265 & 0.0394 & 0.0407 & 0.0578 \\  & CORR & 0.9829 & 0.9655 & 0.9058 & 0.7149 & 0.8245 & 0.7695 & 0.7929 & 0.7891 & 0.8708 & 0.8389 & 0.8192 & 0.8679 & 0.8609 & 0.8725 & 0.828 & 0.7675 \\ \hline \multirow{2}{*}{GRU} & RRMSE & 0.2058 & 0.2832 & 0.3726 & 0.464 & 0.4928 & 0.499 & 0.5037 & 0.5045 & 0.0776 & 0.0903 & 0.0971 & 0.102 & 0.0195 & 0.258 & 0.0347 & 0.0447 \\  & CORR & 0.986 & 0.9601 & 0.9289 & 0.8857 & 0.851 & 0.8465 & 0.8413 & 0.8428 & 0.9412 & 0.9222 & 0.9088 & 0.9079 & 0.9768 & 0.9664 & 0.9534 & 0.9355 \\ \hline \multirow{2}{*}{LSTNet-skip} & RRMSE & 0.1843 & 0.2559 & 0.3254 & 0.4643 & 0.4777 & 0.4893 & 0.495 & 0.4973 & 0.0864 & 0.0910 & 0.1070 & 0.0226 & 0.028 & 0.0356 & 0.0449 \\  & CORR & 0.9843 & 0.969 & 0.9467 & 0.8807 & 0.8721 & 0.869 & 0.8614 & 0.8588 & 0.9283 & 0.9135 & 0.9077 & 0.9119 & 0.9735 & 0.9688 & 0.9511 & 0.9354 \\ \hline \multirow{2}{*}{TPA-LSTM} & RRMSE & 0.1803 & 0.2347 & 0.3234 & 0.4389 & 0.4487 & 0.4658 & 0.4641 & 0.4765 & 0.0823 & 0.0916 & 0.0964 & 0.1006 & 0.0174 & **0.0241** & 0.0341 & 0.0444 \\  & CORR & 0.985 & **0.9742** & 0.9487 & 0.9081 & 0.8812 & 0.8717 & 0.8717 & 0.8629 & 0.9439 & 0.9337 & 0.925 & 0.9133 & 0.979 & 0.9709 & 0.9564 & 0.9381 \\ \hline \multirow{2}{*}{MTGNN} & RRMSE & 0.1778 & 0.2348 & 0.3109 & 0.4277 & 0.4162 & 0.4754 & 0.4461 & 0.4355 & 0.0745 & 0.0878 & 0.0916 & 0.0953 & 0.0194 & 0.0259 & 0.0349 & 0.0456 \\  & CORR & 0.9852 & 0.9726 & 0.9509 & 0.9031 & **0.8963** & 0.8667 & 0.8794 & 0.881 & 0.9474 & 0.9316 & 0.9278 & 0.9234 & 0.9786 & 0.9708 & 0.9551 & 0.9372 \\ \hline \multirow{2}{*}{SCINet} & RRMSE & 0.1775 & **0.2301** & **0.2997** & **0.4081** & 0.2416 & **0.4414** & 0.4495 & 0.4453 & 0.0748 & 0.0485 & 0.0926 & 0.0976 & 0.018 & 0.0247 & 0.034 & 0.0442 \\  & CORR & 0.9883 & 0.9739 & **0.955** & **0.9112** & 0.892 & **0.8890** & **0.8977** & **0.8825** & **0.9492** & **0.9386** & **0.9304** & **0.9274** & 0.9739 & 0.9662 & 0.9487 & 0.9255 \\ \hline \multirow{2}{*}{MDST-GNN} & RRMSE & **0.1764** & 0.2321 & 0.3082 & 0.4119 & **0.4162** & 0.4461 & **0.4377** & **0.4452** & **0.0738** & **0.0833** & **0.0884** & **0.0922** & **0.0172** & 0.0245 & **0.0337** & **0.0431** \\  & CORR & **0.9855** & 0.9735 & 0.919 & 0.9103 & 0.8958 & 0.8803 & **0.8841** & 0.8792 & 0.9454 & 0.9346 & 0.9264 & 0.9222 & **0.9811** & **0.9727** & **0.9578** & **0.9392** \\ \hline \hline \end{tabular} Note: The predicted optimal results are in bold black, and the suboptimal results are shown in red.  
\end{table} 
Table 3: Comparison of forecasting methods for multivariate time series methods. Figure 9: RRMSE comparison of all methods in Electricity and Traffic. Left (**a**) is the RRMSE result of all methods in Electricity, right (**b**) is the RRMSE result of all methods in Traffic, and horizon takes 3, 6, 12, and 24 respectively. However, the model performed slightly worse on the prediction task of Solar Energy data. As can be seen from Figure 12, the periodic pattern is captured by the model well, but there is an error between the results and the truth value within the periodic time. This is because the fluctuation in the data at a certain moment causes the periodic information to be disturbed. In Figure 6, it can be seen that the data remain periodic, but the data fluctuate greatly in a certain period of time.