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Reconcile forecasts for a company, two regions and four stores
Part of the ML System Design Interview path →
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A retailer has seven independently produced next-week forecasts: Total, Region A, Region B, and stores A1, A2, B1, B2 (A1 and A2 sit in A; B1 and B2 in B). In the order (Total, A, B, A1, A2, B1, B2) the forecasts are \hat y=(210,110,102,41,60,30,71).
- Write the summing matrix S and show the forecasts are incoherent. Quantify the gaps.
- Compute the bottom-up forecast for the seven series.
- State the MinT reconciliation formula, explain it in words, and say what W you would use for a hierarchy of 1.2 million bottom series.
- Explain why seasonal naive base forecasts need no reconciliation, and why reconciling quantile forecasts by the same matrix is invalid.
- Your reconciled forecast has a worse sum of absolute errors than the base on last week's data. Is MinT broken? What do you check?
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