Forecasting Weekly Depression Incidence in Mexico: A Multi-Model Framework with Auditable Per-Series Model Selection

Weekly forecasting of psychiatric demand is hard because surveillance signals are heterogeneous across regions, sexes and time, so no single forecasting paradigm performs uniformly well. Rather than impose one algorithm across an entire surveillance system, we present a deterministic, auditable framework that selects, for each series, the model best supported by its own evidence. The framework draws on a library of forecasters with deliberately different inductive assumptions — a structural additive decomposition, a probabilistic recurrent network and two tree-based hybrids — so the candidate pool spans diverse temporal representations and improves coverage across this heterogeneity. A transparent rule then picks one model per series on cross-validated accuracy, reassigns low-incidence series to a regional model, and records every decision in a justified selection log. We instantiate it for weekly incidence of depression (CIE-10 F32) across the 32 Mexican federal entities, drawing on the public bulletins of the National Epidemiological Surveillance System (SINAVE), and validate it twice: by rolling-origin cross-validation over a decade of weekly observations and by a prospective out-of-sample assessment against the 2026 bulletins released after the training cut-off. The resulting assignment concentrates on the recurrent model for most federal-entity series while retaining simpler models where aggregation favours them, and the separately locked national forecast tracks the early-2026 bulletins. Because cross-validated accuracy need not persist as the live signal shifts, the selection is revisable — it re-selects as new bulletins arrive — so the system stays auditable and accountable in deployment, not a frozen leaderboard winner. It is reproducible and extends to other conditions with heterogeneous behaviour.