Electrodermal activity (EDA), commonly measured as skin conductance (SC), is a widely used physiological signal in psychological research and behavioral health applications. EDA is considered an indicator of arousal, a key aspect of emotion and stress. This work proposes a data-driven dynamic system model that characterizes the temporal dynamics of skin conductance and infers the latent arousal signal, utilizing techniques from system identification and sparse optimization. It introduces a fourth-order, linear time-invariant model for the overall skin conductance signal, including both the tonic and phasic components. The model was applied to a large dataset of over 200 participants to evaluate model fit. Furthermore, a three-component decomposition of skin conductance is introduced, based on mathematical definitions derived from the model, which provides key insights into the temporal dynamics of skin conductance. Comparative evaluation shows that the estimated latent neural signal effectively differentiates between high and low arousal states, while maintaining expected physiological properties. This work lays the foundation for numerous behavioral health applications and paves the road for designing physiology-based interventions aimed at regulating arousal.