# Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network
## 4 Experiment Analysis  
### Experiment Dataset Analysis  
In order to evaluate the effectiveness and generalization ability of the model, a classical multivariate time series dataset is adopted in this paper. The dataset comes from the experimental dataset given by LSTNet [19]. It contains multivariate time series datasets in four different domains:  
Figure 3: Model structure diagram of MDST-GNN.  
* Solar Energy: Solar power generation data from Alabama State PV plants in 2006, sampled every 10 min from 137 PV plants;
* Traffic: Hourly road occupancy (between 0 and 1) on San Francisco Bay Area highways for 48 months (2015-2016) recorded by the California Department of Transportation, including data from 862 sensor measurements;
* Electricity: The hourly electricity consumption (kWh) of 321 users from 2012 to 2014;
* Exchange Rate: Daily exchange rate records for 8 countries (Australia, British, Canada, China, Japan, New Zealand, Singapore, and Switzerland) from 1990 to 2016.  
Table 1 presents the statistical information of the experimental dataset in this paper. It includes four data sets. Time length represents the time length of a sequence. Variable represents the number of sequences in a multivariate sequence, and Sample rate represents the time interval of data recording. For example, there are 862 sequences with a length of 17,544 in the Traffic dataset, and the sequence data are recorded at an hourly interval.  
The dataset contains linear and nonlinear interdependencies. The characteristics of the datasets are shown by selecting two variables from each dataset. The power consumption values of the two users at different times is shown in Figure 4. The traffic road occupancy values of the two roads at different times are shown in Figure 5. The horizontal axis represents the different time periods of each day. The vertical axis represents electricity consumption and road occupancy during this period.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Time Length** & **Variable** & **Sample Rate** \\ \hline Solar Energy & 52,560 & 137 & 10 min \\ Traffic & 17,544 & 862 & 1 h \\ Electricity & 26,304 & 321 & 1 h \\ Exchange Rate & 7588 & 8 & 1 day \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dataset Statistics.  
Figure 4: Consumer electricity consumption per hour.  
Figure 5: Road occupancy rate per hour.  
The power generation values recorded every 10 min at both power stations are shown in Figure 6. Daily exchange rate values for the two countries are shown in Figure 7. The horizontal axis represents the time span in different units. The vertical axis represents power generation and exchange rate values during this period.  
From the above data analysis, the data characteristics of the four data sets can be found. As can be seen from the figure, the Traffic, Electricity, and Solar Energy datasets have strong periodic patterns. The time series periods of multiple variables are not exactly the same, but the values of multiple variables at different periods are very similar. The above data analysis results are instructive to this paper. A multivariate time series forecasting model MDST-GNN is proposed in this paper, which can fully utilize the similarity information in the data. Information filtering is enhanced by incorporating attention methods, and the down-sampling convolution module is added to improve the deep information extraction ability. The relationship between multiple variables is modeled through a graph neural network to capture the dependency information between variables. The dependency information obtained by the graph neural network can enhance the forecasting ability of periodic time series.