Investigation and prediction of the linearity of selected solar and geomagnetic activity indices

In this thesis, the nonlinear properties, causal relationships, and future behavioral predictions of selected solar (SSN, F10.7) and geomagnetic (aa, Dst) activity indices, which reflect the interactions between the Sun and the Earth, are examined. Solar activity is of great importance because of the shapes space weather conditions and its impact on technological systems deployed on and around the Earth. Therefore, understanding the intrinsic chaotic nature of solar cycles and uncovering the causal structures among related indices play a vital role in both enhancing the understanding of system dynamics and improving prediction models. There have been many studies in the literature on the relationships between solar and geomagnetic activity indices, and in recent years there has been strong evidence that these relationships can be explained by nonlinear dynamics. In this study, monthly mean values of SSN, F10.7, aa, and Dst indices, the nonlinear properties of the series were analyzed by Hurst exponent, Lyapunov exponent, and correlation dimension methods, the causal relationships between the indices were evaluated by Convergent Cross Mapping (CCM) method, and predictions for Solar Cycle 25 and the next Solar Cycle 26 were performed using Simplex Projection method. The analysis results revealed that both solar and geomagnetic activity indices used in this study exhibit positive autocorrelation, long-term memory, and deterministic chaotic behavior. Causality analysis demonstrated that SSN has a directional and statistically significant influence on both the aa and Dst indices. The prediction results showed that the Simplex Projection method gives very successful results for short-term, mid-term, and relatively long-term predictions of solar and geomagnetic activity.