**Table 8.** Decision lag order.

Note: \* indicates the lag order selected by the corresponding information criterion.

#### 4.3.2. Stationary Test

In order to ensure the stability of the model, it was also necessary to test the stationarity of the model. As shown in Figure 6, all unit roots were in the unit circle, indicating that the model is stable.

**Figure 6.** Stationary test.

## 4.3.3. Granger Causality Test

The Granger test can analyse the causal relationship and action direction of variables in time. It can be seen from Table 9 that the comprehensive index of the atmospheric environment system is the Granger cause of the comprehensive index of the industrial system, and the assumption that the comprehensive index of the industrial system is not the Granger cause of the comprehensive index of the atmospheric environment system cannot be rejected. This is consistent with the optimisation requirements of the industrial system for the strategic improvement of the atmospheric environment system mentioned in the theoretical analysis framework of this paper. From the results of coupling and coordination, it can be seen that the development synchronisation of the two systems in Taiyuan needs to be strengthened. Therefore, Taiyuan should continue to optimise its industrial system, so as to enhance its role in the atmospheric environment system.

**Table 9.** Granger causality test results.

