Historical masonry structures face increasing threats from changing weather patterns and seismic activity, particularly heritage walls suffering from insufficient maintenance. This study investigates the structural behavior of Gubbio's medieval walls in Italy, analyzing correlations between inclination variations and seismic events using a 3-year dataset from Structural Health Monitoring stations. The research applies a hybrid time-series decomposition methodology to isolate trends, seasonality, and residuals of the measurements, while integrating CUSUM analysis to detect potential structural shifts. Seismic data from the National Institute of Geophysics and Volcanology is processed and overlaid with the residuals in order to identify possible correlations. Results reveal that the medieval walls exhibit complex multi-timescale response mechanisms, with residuals showing significant excursions beyond statistical control limits and a persistent directional bias. Notably, substantial cumulative deviations occur in temporal proximity to seismic events, suggesting these structures manifest delayed rather than immediate responses to seismic excitations. The study demonstrates the utility of advanced time-series analysis techniques for enhancing heritage structure monitoring, providing a replicable Python-based workflow framework. This research contributes to heritage conservation by enabling detection of subtle structural changes, while establishing a foundation for future studies incorporating finite element modeling and multivariate analysis to better understand complex environmental-structural interactions in historically significant masonry structures.