Multifractal detrended cross-correlation coefficient for cosmic ray and sunspot time series

This study delves into the multifractal cross-correlations between cosmic ray intensity and sunspot numbers, addressing the shortcomings of traditional correlation analyses that often fail to capture the intricate and multifractal nature of these time series. Cosmic rays and solar activity are critical components of space weather dynamics, and understanding their interactions is essential for predicting space weather events that can affect satellite operations, communication systems, and even climate on Earth. We employ Multifractal Detrended Cross-Correlation Analysis (MFDCCA) to explore these complex relationships across a range of time scales. Our methodology involves segmenting the time series into windows of varying lengths, from 50 to 3900 days, and calculating cross-correlation coefficients for different polynomial fitting orders and fluctuation orders $q=[0.5,1,2,3,4,5]$, using polynomial orders of 2, 3, 4, and 5. This approach allows us to capture the multifractal properties and temporal dependencies within and between the series.

Our analysis reveals significant multifractal correlations, with the highest correlation coefficient of 0.876 occurring for $q=0.5$ and polynomial order 2 with a lag of 57 days. The results demonstrate that higher polynomial orders result in more stable and robust coefficients, indicating stronger correlations on larger scales. These findings highlight the efficacy of advanced techniques like MFDCCA in uncovering the complex interactions between cosmic rays and solar activity, which are often missed by conventional methods. The implications of our study extend to the enhancement of space weather prediction models. By incorporating additional heliophysical variables such as solar wind conditions, interplanetary magnetic field data, and indices of coronal mass ejections or solar flares, future research can construct more comprehensive models that better capture the multifractal interactions governing these phenomena. This expanded understanding is crucial for improving the accuracy of space weather forecasts and mitigating the potential impacts of space weather events on technological and natural systems.