Earthquake prediction remains a critical challenge in geophysics and geochemistry. This study explores the potential of radon, a naturally occurring radioactive gas, as a geochemical indicator for earthquake prediction, focusing on Taiwan—a region of high seismic activity. Radon data were collected from a soil-gas data monitoring stations network with hourly measurements, creating a high-resolution dataset. A key challenge in using radon for earthquake forecasting is the influence of meteorological factors, particularly rainfall, which can obscure earthquake-related radon variations. To address this, advanced statistical techniques, including Singular Spectrum Analysis and digital filtering, were employed to remove meteorological influences while preserving short-term variations. Analysis of radon data from the Hsinhua monitoring station revealed dominant daily variations accounting for 19% of the total variance, primarily influenced by atmospheric temperature through the “Capping Effect.” At the San-Jie monitoring station, decomposition of the hourly radon time series into seasonal trend, and residual components effectively identified anomalous fluctuations linked to regional seismic events. The results demonstrate that accounting for meteorological effects enhances the detection of earthquake-related radon anomalies while distinguishing them from rainfall-induced variations. This study underscores the importance of refining geochemical earthquake prediction models and highlights the effectiveness of advanced statistical techniques in isolating seismic precursors in radon time series.