One hierarchy of time series
The levels of planning are organised as one hierarchy: across products and markets, and across time. Strategic and operational plans become the top and bottom of the same structure, so they can be forecast and reconciled together.
- Market drivers at the topLeading indicators work best on aggregates, where noise is low and the market signal is strong.
- Demand drivers at the bottomPromotions, orders and constraints are known at SKU and week level.
- Small, well-estimated modelsEach level keeps a model that suits its data, instead of one model that does everything badly.
Not top-down, not bottom-up
Top-down throws away what the detail knows. Bottom-up throws away what the market knows. Reconciliation forecasts every level on its own, then combines them with weights chosen to minimise forecast error, under the condition that the levels add up.
- Weights from dataW is estimated from the base forecasts' out-of-sample errors (for example with structural scaling or a shrinkage estimator), so nobody chooses a direction.
- Across time tooTemporal hierarchies make weeks sum to months and months to years, so the operational, tactical and strategic plans agree.
- Better at every levelInformation flows both ways, so even the operational level usually improves.
A worked example
| Market | Group A | Group B | |
|---|---|---|---|
| Base forecasts | 950 | 580 | 460 |
| Sum of groups | 1,040, which disagrees with the market by 90 | ||
| Top-down, historical shares | 950 | 475 | 475 |
| Bottom-up | 1,040 | 580 | 460 |
| Reconciled | 962 | 513 | 449 |
Illustrative. The reconciled numbers add up (513 + 449 = 962), stay close to the market view, and keep the detail that the groups know.
Leading indicators, where they matter
Observing a leading indicator reveals turning points that are not visible in the target series itself, such as the demand for an SKU. The example is an 8-month leading indicator from a case company.
- 1. Qualitative insightIndicators shown to planners. Helps de-bias judgement, but inconsistent and expensive in expert time.
- 2. Explanatory variablesIndicators in the demand models. Noise in disaggregate data makes this hard at SKU level.
- 3. Hierarchical modelsIndicators at the level where they have the most impact, reconciled down. This is Indicio One.
Variable selection searches over 400 million series from the world’s leading data providers, through Indicio Connect, testing lags and transformations, and ranks indicators by their contribution to out-of-sample accuracy rather than by correlation.
Illustrative redraw of a case-company example.
Models and evaluation
Every forecast is built from a library of 80+ models, evaluated out of sample, and combined by accuracy.
ARIMA, ETS, Theta, STL, TBATS, Prophet and neural networks.
Read moreEconometricMultivariateVAR, VECM, VARMA and ARDL, using relationships between variables.
Read morePenalizedMany predictorsRidge, Lasso, Elastic Net, group lasso and hierarchical VAR.
Read moreMixed frequencyNowcastingMIDAS variants that use high-frequency data for low-frequency targets.
Read moreMachine learningNon-linearANN, LSTM and GRU.
Read moreExplainabilitySHAP valuesEach forecast decomposed into the contribution of each driver.
Read moreThe evidence
Peer-reviewed, on a global manufacturer's data: putting leading indicators at the top of the forecast hierarchy, instead of a history-only forecast at SKU level, lowers forecast error, and the gain grows with the horizon.
| Lead time | History-only (E) | Indicators at the top of the hierarchy (LEE) | Lower error |
|---|---|---|---|
| 3 months | 2.048 | 1.936 | 5.5% |
| 6 months | 3.931 | 3.620 | 7.9% |
| 12 months | 8.005 | 6.817 | 14.8% |
Cumulative RMSSE at SKU level, from Table 2 in Sagaert & Kourentzes (2025), Omega 136, 103335 (open access). E is univariate ETS; LEE is the hierarchical model with leading indicators. Inventory: Section 5.2, Figures 5 and 6.
Nikolaos Kourentzes, co-author of the research, works with Indicio.
References
- Kourentzes, N. (2022). Toward a one-number forecast: cross-temporal hierarchies. Foresight, 67.
- Kourentzes, N. & Athanasopoulos, G. (2019). Cross-temporal coherent forecasts for Australian tourism. Annals of Tourism Research, 75, 393–409.
- Athanasopoulos, G. & Kourentzes, N. (2023). On the evaluation of hierarchical forecasts. International Journal of Forecasting, 39(4), 1502–1511.
- Sagaert, Y. R. & Kourentzes, N. (2025). Inventory management with leading indicator augmented hierarchical forecasts. Omega, 136, 103335.
- Kourentzes, N. (2026). Forecast reconciliation under observational incoherence. Working paper.
- Lee, H. L., Padmanabhan, V. & Whang, S. (1997). Information distortion in a supply chain: the bullwhip effect. Management Science, 43(4), 546–558.