Analysis of Galactic Cosmic Ray Variability and Time-Lagged Relation to Solar Activity

The study of galactic cosmic ray variations and their connection to solar activity has been explored using various methods, such as cross-correlation analysis, which measures the synchronization between time series peaks, and power spectral density or wavelet analysis. In this work, we investigate the potential of advanced signal processing techniques, specifically Empirical Mode Decomposition and the Hilbert Transform, which are well-suited for handling the non-linear and non-stationary nature of cosmic ray modulation. These methods enable the study of phase coherence and provide a refined approach to extracting key time-dependent spectral features from cosmic ray observations and solar proxies across different energy, temporal, and frequency ranges. Using a multi-experiment dataset from ACE/CRIS, neutron monitors, and the latest AMS-02 measurements, we examine the time lag between cosmic ray measurements and solar proxies, comparing the results with those obtained from well-established methods. Our analysis highlights the evolution and patterns of the time lag, provides qualitative confirmation of the charge-sign dependence, and demonstrates the direct role of drift in shaping these effects. These findings are fundamental for the development of cosmic ray flux forecasting models based on solar activity proxies and are aimed at improving radiation risk estimations in the upcoming era of human space exploration.