Bottom-Up Reconciliation

Forecasts are generated at the lowest hierarchical level—such as individual SKU-location combinations—where demand patterns are most distinct. This prevents the dilution of variance that occurs when forecasting at aggregate levels, where unique product behaviors are averaged out. By modeling each bottom-level series independently, the approach captures local trends, seasonality, and intermittent demand patterns that would be invisible in top-down methods.

Once base forecasts are produced for each bottom-level node, they are summed upward through the hierarchy using a summing matrix. This matrix defines the structural relationships between levels—for example, how individual product forecasts roll up into category totals, then regional totals, and finally national aggregates. The result is perfect mathematical coherence: the sum of all child node forecasts exactly equals the parent node forecast, eliminating reconciliation discrepancies.

While simple summation ensures coherence, it ignores forecast error covariances. The Minimum Trace (MinT) method optimally reconciles base forecasts by minimizing the trace of the forecast error covariance matrix. This approach:

• Accounts for correlated errors between series
• Produces the most accurate reconciled forecasts theoretically possible
• Requires estimating the full covariance structure of base forecast errors

In top-down reconciliation, a single forecast is generated at the highest aggregate level and then disaggregated downward using historical proportions. This approach:

• Risks masking granular anomalies in the averaging process
• Assumes static distribution patterns that may not hold under market shifts
• Is computationally simpler but sacrifices bottom-level accuracy Bottom-up is preferred when granular decision-making—such as SKU-level replenishment—is critical.

Bottom-up reconciliation is particularly effective for intermittent demand patterns common in spare parts and long-tail retail. At the aggregate level, intermittent series may appear smooth, but the underlying zero-inflated behavior requires specialized models like Croston's method. By forecasting at the granular level where zeros are explicit, bottom-up approaches avoid the bias introduced by aggregating sparse data before modeling.

Modern bottom-up reconciliation extends beyond point forecasts to probabilistic distributions. Each bottom-level node produces a full predictive distribution, and these are aggregated coherently to produce hierarchically consistent prediction intervals. This enables risk-aware inventory decisions at every level—from setting safety stock for individual SKUs to quantifying aggregate portfolio exposure—while maintaining mathematical coherence across the entire hierarchy.