# Multivariate Time Series Data Prediction Based on ATT-LSTM Network
## 4 Experiment
### Experimental Results and Analysis
#### 4.3.1 Model Comparison  
We compare the ATT-LSTM model with the other six models (VAR, LSTM, GRU, LSTM+Zoneout, LSTM-RNN, Attention-RNN) to prove the effectiveness of the ATT-LSTM model. Based on two evaluation indicators, MAE and RMSE, we show the best results of the model. The results are shown in Table 3. The comparison result is shown in Figure 7.  
According to the comparison results in Table 3 and Figure 7, we can draw the following conclusions:  
1. Three baseline models (VAR, LSTM, GRU). On the Nasdaq 100 dataset, the LSTM performed best, followed by the VAR model. The gated recurrent unit (GRU), as a simpler variant of the LSTM, has not achieved better prediction results on this data set. The LSTM is still the best performer on the Beijing PM2.5 dataset, but the difference between the three models is insignificant.
2. Three variant models (LSTM+Zoneout, LSTM-RNN, Attention-RNN). The LSTM+Zoneout model performed best on the Nasdaq 100 dataset, followed by the Attention-RNN model. The combination of the attention mechanism and RNN has greatly improved the ability of the RNN to process multivariate data. However, due to the characteristics of the RNN, the processing of multivariate time series data has not reached the desired effect.
3. The performance of the three baseline models (VAR, LSTM, GRU) on the Nasdaq 100 dataset is worse than that on the Beijing PM2.5 dataset because the three baseline models do not analyze the correlation between multivariate sequences. The correlation sequence of the NASDAQ 100 dataset is far greater than that of the Beijing PM2.5 dataset, which causes some interference to the three baseline models, making the effect of the three baseline models on the NASDAQ 100 data set low the impact of the Beijing PM2.5 dataset. On the contrary, the three variant models (LSTM+Zoneout, LSTM-RNN, Attention-RNN) analyze related sequences. The overwhelming number of related sequences in the Nasdaq 100 dataset provides the three models with more robust learning capabilities, making the three models perform better on the Nasdaq 100 dataset than the PM2.5 dataset.
4. The ATT-LSTM model has achieved good results on both datasets. On the Nasdaq 100 dataset, compared to the best-performing LSTM baseline model, the ATT-LSTM model has about 70% improvement, compared to the best-performing LSTM+Zoneout change model, ATT-LSTM model has about 40% improvement. On the Beijing PM2.5 dataset, the ATT-LSTM model has also achieved performance improvements compared to other models, but the improvement is lower than in the Nasdaq 100 dataset.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Dataset**} \\ \cline{2-5}  & \multicolumn{2}{c}{**NASDAQ 100**} & \multicolumn{2}{c}{**PM2.5 of Beijing**} \\ \cline{2-5}  & **MAE** & **RMSE** & **MAE** & **RMSE** \\ \hline VAR & 0.7012 & 0.9134 & 0.6538 & 0.7986 \\ LSTM & 0.6974 & 0.8965 & 0.6328 & 0.7245 \\ GRU & 0.9567 & 0.9981 & 0.6728 & 0.7457 \\ LSTM+Zoneout & 0.3665 & 0.4203 & 0.5769 & 0.6867 \\ LSTM-RNN & 0.5439 & 0.6268 & 0.6364 & 0.7842 \\ Attention-RNN & 0.4056 & 0.4938 & 0.4241 & 0.5178 \\ ATT-LSTM & 0.1948 & 0.2633 & 0.2134 & 0.2956 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison result table.