Time series and forecasting · insight-1224
Add non-negativity to reconciliation when the series are counts or sales
- Evidence type
- empirical finding
- Difficulty
- medium
- Roles
- Data scientist, ML engineer
- Industries
- retail, aviation
Summary: situation, action, reason, boundary
Situation
Route forecasts from a model are all non-negative, but after MinT reconciliation a thin route shows -3 passengers on some days.
Action
Check the reconciled output for negatives in the backtest, and if they occur reconcile with non-negativity constraints (a quadratic programme) or use a method that preserves it. Verify that coherence still holds to tolerance.
Reason
Unconstrained least-squares reconciliation can move a small series below zero even when all base forecasts are positive.
Boundary
Hierarchies containing small, intermittent or low-volume bottom series.
Symptom or risk
Negative values break downstream rules, and clipping them to zero after the fact breaks the aggregation constraints, so totals no longer add up.
Exceptions
Series that can be legitimately negative (net flows, profit).
Trade-offs
Constrained solves are slower; in the authors' tourism study the gains were slight at the lowest level and slight losses at aggregate levels.
Pitfalls
Clipping the reconciled values and publishing totals that no longer match.
Lessons and concepts
Claims and their sources
MinT and its variants do not guarantee non-negative coherent forecasts; adding non-negativity constraints solves a quadratic programme and gave slight gains at the most disaggregated level and slight losses at aggregate levels in a tourism study.