## 4 Results
### Performance Comparison  
Figure 4 shows the actual imputation effect of our proposed model on the electricity dataset. The upper half is the time series imputation value, the lower half is the time series real value, and the red dots describe the missing data. Under the high missing rate, our model can still complete high-quality time series imputation, which fully demonstrates the performance of the informer-WGAN model. We also applied the informer-WGAN model on the CMG dataset, and Figure 5 shows the imputation results on the CMG dataset at the missing rates of 20% and 50%. Our proposed method revealed trends in the CMG time series. The pRMSE was 0.583 at the 20% missing rate and still reached 0.729 at the 80% missing rate. This shows that informer-WGAN is suitable for CMG time series imputation. Figures 6 and 7 show the frequency hist of the imputation results and real-time series on the electricity dataset and ETTh1 dataset. The imputation series demonstrates obvious similarity with the real-time series. The frequency hist shows the effect of our imputation model. Figure 8 shows the actual results of different imputation methods on the ETH1 dataset at missing rates of 50% and 80%. Obviously, our informer-WGAN performed better than the other imputation methods such as ARIMA and informer, especially when the missing rate was high. In order to show the actual effect of the model proposed, we chose and compared the traditional data imputation methods, including the ARIMA, the AST model, and the original informer, to compare the data imputation of each model under different missing rates. We also modified the original AST model and compared its effect, and we named it as ST-WGAN. The supplementary results were quantitatively evaluated by the p_RMSE value proposed in the previous section. Figure 6: Frequency hist of imputation results and real-time series on electrity dataset. Figure 7: Frequency hist of imputation results and the real time series on ETHh1 dataset. As shown in Tables 6 and 7, the informer-WGAN model we proposed achieved the best results on both the electricity dataset and the ETTh1 dataset. The traditional ARIMA method had poor imputation performance. Compared with the deep learning method, the traditional method had limited utilization of the temporal features, resulting in poor imputation results. However, the accuracy of the AST method decreased significantly when the missing rate increased. Because the sparse transformer model adopted a step-by-step method during decoding (that is, the value of the next time was based on the imputation value of the previous time), it could not be forwarded at one time. The operation was obtained, and the problem of error accumulation occurred. Therefore, the AST model is not suitable for imputation problems with high missing rates. In the informer model, the concept of generative decoder is proposed, and all the imputation was completed through one forward calculation process. The model we proposed also adopts a similar design, which makes the model suitable for imputation under high missing rates. According to the \(p\_RMSE\) formula in the previous section, when the quality of the generated sequence is poor, due to the introduction of the Pearson correlation coefficient, the performance gap of the model is more significant. Tables 8 and 9 show the RMSE and Pearson correlation coefficient of the imputation results and the ground truth on the electricity and ETTh1 datasets. We note that in the table, the ARIMA algorithm obtained the best RMSE value under the 20% missing rate, but its actual imputation result was not close to the true value, so the Pearson correlation coefficient result was poor. The PRMSE value obtained by combining these two statistics was more conducive to obtaining time series imputation results that met the requirements.