Time series and forecasting · insight-1724
Forecast a monthly series at several temporal aggregation levels and reconcile them
- Evidence type
- empirical finding
- Difficulty
- hard
- Roles
- Data scientist
- Industries
- aviation, retail
Summary: situation, action, reason, boundary
Situation
Monthly route demand is forecast with one model at one frequency, while planners also use quarterly and annual figures that disagree with the monthly sum.
Action
Aggregate non-overlapping periods (1, 2, 3, 4, 6 and 12 months), forecast each level with its own model, and reconcile the levels into coherent forecasts. Compare against the single-level baseline on rolling origins, by level.
Reason
Temporal hierarchies combine forecasts from all aggregation levels, which mitigates model uncertainty and gives one set of numbers across horizons; the authors report the gain is largest when modelling uncertainty is high.
Boundary
Monthly or quarterly series with at least several years of history and decisions at several horizons.
Symptom or risk
The monthly model is noisy, its annual totals drift from the annual model, and each planning horizon works from a different number.
Exceptions
Very short series, where upper levels have too few points.
Trade-offs
More models to fit and monitor, and reconciliation changes the monthly numbers.
Pitfalls
Scoring only the monthly level; fitting weights on data after the origin.
Example
Arithmetic: for a 12-month horizon the levels give 12 + 6 + 4 + 3 + 2 + 1 = 28 forecasts per series, one annual total that the monthly values must sum to.
Lessons and concepts
Claims and their sources
Athanasopoulos, Hyndman, Kourentzes and Petropoulos propose temporal hierarchies built by non-overlapping temporal aggregation, combine forecasts from all levels into temporally reconciled forecasts, and report that this increases accuracy over conventional forecasting, particularly under increased modelling uncertainty (abstract-level reading; evaluated on M3 monthly and quarterly series).