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Hierarchical Retail Demand Forecasting — M5

Business question

Produce coherent SKU × store × week forecasts — a category forecast must equal the sum of its SKUs — to plan shelf replenishment and department buying off the same numbers.

Data & EDA

• Source: M5 Forecasting Accuracy (Kaggle) — Walmart daily sales for ~30k SKUs across 10 stores in 3 states, with calendar, prices, and SNAP events.
• EDA targets:
  • Heavy intermittency (many zero-sales days per SKU)
  • Price/promo sensitivity
  • Holiday effects (Super Bowl, Christmas, Easter)
  • SNAP event-driven demand pulls
  • Hierarchy: SKU → category → department → store → state

Modeling

Level	Approach
Aggregate (national weekly)	SARIMA(1,1,1)(0,1,1)₅₂
Base (item × store)	GradientBoostingRegressor with lag/calendar/rolling features
Reconciliation	MinT-OLS projection across the full hierarchy: TOTAL / STATE (3) / STATE×DEPT (15) / BOTTOM (130)

Validation

• 8-week held-out test, per-series RMSSE at every hierarchy level (not just TOTAL+BOTTOM), each series scaled by its own training-naive error per the canonical M5 WRMSSE protocol.
• Headline numbers:

Level	pre-recon mean RMSSE	post-recon mean RMSSE	Δ
TOTAL (1 series)	3.11	3.13	+0.02 (slightly worsens — pulled toward bottom-up)
STATE (3 series)	2.30	2.25	−0.05 (improves)
STATE×DEPT (15 series)	1.59	1.57	−0.02 (improves)
BOTTOM (130 series)	1.305	1.299	−0.006 (negligible)

What the numbers say: coherence holds by construction (bottom sums match TOTAL by linear algebra). Measurable error reduction only shows up at the mid-levels where MinT typically earns its keep (STATE, STATE×DEPT). TOTAL slightly worsens because reconciliation pulls the SARIMA aggregate toward the bottom-up sum; BOTTOM barely moves.

Deployment sketch

• Weekly batch pipeline: base GBM per (item × store), aggregate SARIMA, MinT-OLS reconciliation, output written as a coherent (level, series, week, forecast) table.
• Consumers: replenishment reads BOTTOM; merchandising reads STATE×DEPT; planning reads TOTAL — all reading the same reconciled numbers.

Business outcome

• One coherent forecast set across TOTAL → STATE → STATE×DEPT → BOTTOM; replenishment, merchandising, and planning no longer argue over which number is correct.
• MinT-OLS lift is modest in absolute terms (hundredths of RMSSE at mid-levels); the operational value is coherence, not accuracy improvement.

Next iterations: WLS / MinT-shrink reconciliation using empirical forecast-error covariances; add M5 calendar price/promo features; evaluate across rolling-origin windows for CI on each level’s RMSSE delta.

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