Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using Chatterjee's correlation coefficient

This study revisits the cross-correlation between cosmic ray intensity (CRI) and solar activity (SA) by comparing traditional Pearson correlation with Chatterjee's correlation coefficient. Traditional analyses using Pearson correlation are useful for identifying linear relationships and time lags. However, they may not fully capture more complex interactions in the data. Chatterjee's correlation coefficient, while sensitive to different types of relationships, including nonlinear ones, provides a complementary perspective on the temporal relationships between CRI and SA. This approach broadens our understanding of potential dependencies, offering additional insights that may not be captured through Pearson correlation alone. The findings reveal that Chatterjee's correlation complements Pearson's insights by providing an alternative view of the relationship between cosmic ray intensity (CRI) and solar activity (SA). The results show that Chatterjee's correlation coefficients are, on average, approximately 45-50% smaller than Pearson's, which could reflect different sensitivities to the underlying data structure rather than solely indicating a nonlinear component. Additionally, the time lags identified using Chatterjee's correlation are generally shorter and more consistent across different solar cycles compared to those obtained with Pearson's correlation, suggesting that CCC may capture temporal patterns in a distinct manner. Further analysis using Dynamic Time Warping (DTW) and Mean Absolute Percentage Error (MAPE) metrics demonstrated that, in more than half of the scenarios considered, alignment based on Chatterjee's time lags resulted in lower errors and better alignment of the series compared to Pearson's lags. This indicates that Chatterjee's method is particularly effective for capturing the immediate and nuanced responses of CRI to SA changes, especially in recent solar cycles. This comprehensive approach provides broader insights into the dynamic interactions between cosmic ray intensity (CRI) and solar activity (SA), highlighting the importance of considering multiple correlation measures, including both linear and nonlinear approaches, in space weather research. The results suggest that Chatterjee's correlation offers a complementary perspective on these interactions, providing additional details about how SA influences CRI over time, which may not be fully captured by Pearson's correlation alone. (c) 2024 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).