## 4 Case Study
### Results of the Causality Test Between Environmental Factors and Electricity Loads  
In order to realize the subsequent causality analysis between the electricity load and the various influencing factors, it is first necessary to carry out the ADF smoothness test for the series of maximum temperature, minimum temperature, average temperature, maximum relative humidity, minimum relative humidity, average relative humidity, maximum wind speed, minimum wind speed, average wind speed, rainfall and load mean. The ADF test results for each feature quantity are shown in Table 1. It can be seen that all the original feature series pass the smoothness test, and the original series is used for causality analysis. Granger causality tests at different quantile levels were performed using the above characterized series that passed the smoothness test. Nineteen isometric quantiles were obtained in [0.05, 0.95], and the lags were set to be 1 day, 2 days, and 3 days, respectively. The causality test values of all influential factors on load at different quartiles with the lag of 1 day are demonstrated in Table 2. It is observed that average temperature, average relative humidity, and average wind speed do not lead to Granger changes in the average load at the 1% significance level, which suggests that these results are robust to the quantile regression model under the null hypothesis of Granger non-causality. Thus, there is no evidence for Granger causality between changes in average temperature, average relative humidity, and average wind speed and changes in load. In quartiles closer to the top and bottom, temperature, humidity, and wind speed show stronger Granger causality with load changes. This suggests that the model detects more significant causal relations under extreme weather conditions compared to moderate weather changes. While the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factors** & **Threshold of 1\%** & **ADF Value** & **Probability** \\ \hline Maximum temperature & \(-1.9424\) & \(-13.294\) & \(0.0010\)** \\ Minimum temperature & \(-1.9424\) & \(-6.8712\) & \(0.0010\)** \\ Average temperature & \(-1.9424\) & \(-3.4273\) & \(0.0010\)** \\ Maximum humidity & \(-1.9424\) & \(-13.049\) & \(0.0010\)** \\ Minimum humidity & \(-1.9424\) & \(-7.4050\) & \(0.0010\)** \\ Average humidity & \(-1.9424\) & \(-5.7568\) & \(0.0010\)** \\ Maximum wind speed & \(-1.9424\) & \(-13.657\) & \(0.0010\)** \\ Minimum wind speed & \(-1.9424\) & \(-6.1659\) & \(0.0010\)** \\ Average wind speed & \(-1.9424\) & \(-6.6557\) & \(0.0010\)** \\ Rainfall & \(-1.9424\) & \(-8.2339\) & \(0.0010\)** \\ Average load & \(-1.9424\) & \(-3.1475\) & \(0.0024\)** \\ \hline \hline \end{tabular} Note. * indicates that the item passes the 0.01 level of significance test.  
\end{table} 
Table 1: ADF test results for the original feature sequence. traditional mean Granger test focuses only on the mean of the conditional distribution, the quantile analysis is able to capture the tail dependencies, highlighting the potential impacts of extreme weather events on electricity loads. Thus, the strength of the quantile framework in identifying key influences is validated, especially in scenarios with sharp load fluctuations or frequent extreme weather events. Meanwhile, when the maximum temperature, the maximum relative humidity and the maximum wind speed are in the middle of the quantile range, there are a small number of intervals in which there are no obvious causal results. This may be due to the fact that the amount of factor characteristics is at an intermediate level, which produces a diversity of influences on human activities and prevents the formation of a more uniform trend of activities. The unpredictable load changes are created by the decentralization of choices, and evidence of Granger causality is demonstrated when these characteristics undergo larger positive or negative, suggesting that these factors lead to changes in loads.