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Bottom-Up, WLS or MinT for the Planning Hierarchy
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Your hierarchy has 1 total, 4 regions, 20 stores, 200 SKUs and 4,000 SKU-store series (4,225 nodes). Base forecasts are produced separately for every node, and they disagree. Pooled over three backtest origins (WAPE by level):
| Method | Total | Region | Store | SKU | SKU-store |
|---|---|---|---|---|---|
| Base | 0.0404 | 0.0727 | 0.1025 | 0.1662 | 0.5886 |
| Bottom-up | 0.0407 | 0.0717 | 0.0990 | 0.1679 | 0.5886 |
| OLS | 0.0389 | 0.0739 | 0.1033 | 0.1667 | 0.5901 |
| WLS, structural weights | 0.0363 | 0.0702 | 0.0988 | 0.1642 | 0.5894 |
| WLS, variance weights | 0.0374 | 0.0691 | 0.0978 | 0.1644 | 0.5886 |
| MinT with shrinkage | 0.0376 | 0.0693 | 0.0980 | 0.1644 | 0.5887 |
The fitted MinT shrinkage intensity toward a diagonal was 0.96 to 0.99, the largest incoherence in the base forecasts was 645 units, and a dense MinT solve took about 21 seconds.
- Why reconcile at all, and how do you test coherence in CI?
- Which method would you ship if orders are placed at SKU-store level? And if regional capacity is the main decision?
- Why did MinT behave like WLS here, and does that scale to 25 million series?
- Reconciliation produced negative bottom-level forecasts in some cells. What do you do?
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