# Prediction of Air Quality Combining Wavelet Transform, DCCA Correlation Analysis and LSTM Model
## 3 Results
### DCCA-LSTM Predictive Analysis at Short-Medium and Long Scales
#### 3.3.1 Short-Scale Application of the DCCA-LSTM Model  
This part analyzes, at short scales, the prediction effects of 24 h, 48 h, and 168 h time steps after screening critical inputs with DCCA coefficients, so as to have short-range practical significance.  
Table 2 displays the A-T, A-H, A-P, and A-W coefficients at short scales for the 24 h, 48 h, and 168 h windows that were used to filter the model input characteristics. For instance, because the A-W coefficients for the 24 h period and the A-P coefficients for the 48 and 168 h periods were less than \(-0.2\), no wind speed data were entered for the 24 h period, and no barometric pressure data were entered for the 48 and 168 h periods.  
As demonstrated in Figure 4, the LSTM model based on wavelet transform and DCCA correlation coefficients was experimentally plotted against the true and predicted AQI values on the test set; the vertical coordinates represent the AQI values, the horizontal coordinates represent the time series, the solid blue line represents the true sample data values, and the solid orange line represents the predicted values of the model at the next time step.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Window-Size** & **A-T** & **A-H** & **A-P** & **A-W** \\ \hline
2  
Figure 4 uses data from the preceding 24 h, or one day, to estimate the AQI value at the following step when the A-W coefficient was less than 0.2. From Table 2, since the A-W coefficient was \(-0.125\), it fell within the interval [\(-0.2\), 0.2], indicating that there was a low correlation between the wind speed data and the AQI representation. Thus, the wind speed data were omitted. Figure 5 uses data from the preceding 48 h or two days to estimate the AQI value at the following moment when the A-P factor was less than 0.2, which was inconsequential, and omits pressure data as a result. Figure 6 uses data from the past 168 h or week to estimate the AQI value at the following instant when the A-P coefficient was equal to \(-0.09\), which was not significant, and omits pressure data.  
Figure 4: 24 h comparison of forecasts. (**a**) Results of prediction without DCCA feature screening. (**b**) Prediction outcomes following DCCA feature screening.  
Figure 5: 48 h comparison of forecasts. (**a**) Results of prediction without DCCA feature screening. (**b**) Prediction outcomes following DCCA feature screening.  
Figure 6: 168 h comparison of forecasts. (**a**) Results of prediction without DCCA feature screening. (**b**) Prediction outcomes following DCCA feature screening.  
Using the mean squared error (MSE) to test the model's correctness, the statistics in Table 3 indicate that the window size equal 24 LSTM model with DCCA coefficients to filter the variables reduced the mean squared error by around 0.01 and improved the running time by approximately 1 s. When the window size was 48, the mean square error decreased by 0.016 and the efficiency increased by 2 s. When the window length was 168, the mean square error decreased by 0.02 and the efficiency increased by 4 s.