This paper is an attempt to gain mathematical insight into the aggregateâ€“disaggregate intermittent demand approach (ADIDA) forecasting framework, by formulating it as a multi-rate signal processing system. After a brief synopsis of the framework's background, an alternative way to perceive ADIDA from a systemic viewpoint is derived by breaking down its managerial steps into fundamental and well-studied components. Mathematical properties stemming from each separate system block are thoroughly explored and their practical effects are then exemplified through simulated paradigms of common time series patterns. Subsequently, theoretical and practical evidence are combined to draw useful conclusions about the framework's performance and make suggestions on its application. Finally, guidelines for further research are proposed.