Nonlinear and Causal Dynamics between Solar and Geomagnetic Activity Indices: Findings from Chaos and Causality Measures

This study aims to identify nonlinear/chaotic features and causal relationships among monthly SSN, F10.7, aa, and Dst indices over December 1963-March 2025. Phase-space is reconstructed via AMI-selected delay tau and FNN dimension E; we estimate the Hurst exponent H, the largest Lyapunov exponent lambda, and the correlation dimension D-2; and apply CCM with SSN as reference. H spans 0.84-0.93 (SSN approximate to 0.93; F10.7 approximate to 0.93; aa approximate to 0.88; Dst approximate to 0.84), indicating strong persistence. lambda ranges from approximate to 0.010 to approximate to 0.040 (highest for Dst, lowest for aa), implying deterministic chaos with finite prediction horizons. D-2 varies between 3.37- 3.86, consistent with low-moderate dimensional structure. CCM analysis shows a strong linear relationship between SSN-F10.7, while indicating a non-linear causal relationship between SSN and other indices. In conclusion, sunspot variability affects global geomagnetic activity continuously and nonlinearly on a monthly scale; this effect is most pronounced for aa and weaker for Dst.