## 3 Results and Discussion of Data Analysis
### Granger Causality Test Analysis  
In Section 3.2, the correlation analysis revealed both linear and nonlinear relationships between C-class XRA events and low-frequency signal strength. However, correlation does not imply causality. To further investigate whether XRA events are the causal drivers of changes in low-frequency signal strength, we applied the Granger causality test. The Granger causality test is a statistical method based on the predictive capability of time series data, used to assess whether the historical values of one variable can significantly predict the future values of another [7]. In this study, this approach allows us to assess whether changes in XRA are causally related to fluctuations in signal strength over time. The results of the Granger causality test are expressed in terms of \(p\)-values. Smaller \(p\)-values indicate a stronger statistical significance of the causal relationship. Typically, a \(p\)-value of less than 0.05 is considered to indicate a significant Granger causal relationship. For example, in the data used in this study, a sample with a lag of 50 s corresponds to a Granger \(p\)-value of 0.0007, suggesting that even with a relatively short lag time, the influence of XRA on signal strength remains statistically significant. This study investigates the causality between signal strength and XRA data in 5-min intervals, specifically analyzing the differences in causality before and after solar storm events. The average percentage of \(p\)-values below 0.05 for each time interval was calculated as a measure of significance, used to evaluate the strength of the causal relationship in each period. The results of the significance evaluation show that the \(p\)-values in the lag intervals of \((-5,0)\) and \((0,5)\) minutes are notably lower, indicating the strongest Granger causality between XRA and signal strength during these periods, as shown in Figure 7. In the negative lag intervals \((-20\) to \(0\) min), the significance level increases from 13.33% to 60%, suggesting that when changes in low-frequency signal strength precede changes in X-ray flux, the Granger causality gradually intensifies. This phenomenon supports the hypothesis that the ionospheric response to low-frequency signals may occur before changes in X-ray  
Figure 6: Distribution Statistics of Solar Storms of Different Intensity Levels and Correlation Coefficients. flux. In the intervals of \([-10,\,-5)\) and \([-5,\,0)\), the significance levels are 41.25% and 60%, respectively. These elevated significance values suggest that variations in low-frequency signal strength could represent an early response to an impending XRA event. These findings support the earlier argument regarding the sensitivity of low-frequency signal strength to early ionospheric disturbances. Even before the solar storm reaches C-class levels, changes in signal strength can already detect ionospheric ionization effects induced by X-ray radiation. However, while the significance levels of 41.25% and 60% suggest some degree of correlation, they are not exceptionally strong. It is crucial to emphasize that Granger causality identifies statistical causality but does not confirm physical causality. This distinction highlights that while these results point to a potential relationship, they should not be interpreted as conclusive evidence of a direct physical link. Therefore, these findings should be viewed as a basis for further exploration, rather than definitive proof. For the positive lag intervals (0 to 20 min), the significance in the intervals of \([0,5)\) and \([5,\,10)\) is 66.67% and 70%, respectively, marking the periods with the highest significance. This indicates a strong Granger causal relationship between the increase in X-rays and the subsequent changes in low-frequency signal strength. After 10 min, the significance starts to decline, but the correlation remains relatively high (e.g., 53.33% in the interval [10, 15)]. This suggests that the impact of XRA events can still be observed for a period after their occurrence.