From Entity Rollouts to Aggregate Forecasts: Generative Process Models for Production Temporal Systems

Many temporal systems involve entities that deplete gradually through recurring events. Forecasting in such systems requires both per-entity predictions and aggregate projections across cohorts, yet these are typically served by separate models, and aggregate-level approaches are often data-starved. We introduce DFMTPP (Discrete Fractional Marked Temporal Point Process), a generative framework that models the per-entity consumption process by predicting at each period whether a consumption event occurs and what fraction of remaining value is consumed, chaining these into a survival function. We demonstrate on a proprietary portfolio of depletable financial instruments and on the public Freddie Mac mortgage dataset. A single model trained on this per-entity objective serves three purposes at once: it predicts per-entity residual value more accurately than gradient-boosted baselines, it produces cohort-level aggregate forecasts (by summing individual survival rollouts) whose wMAPE is up to 4.6× lower than aggregate-level time-series models, and it learns transferable representations for unseen downstream tasks. The system is deployed in production at scale.