Hierarchical forecasting

Different people need the forecast at different levels. A warehouse planner needs SKU by location by week. A regional sales head needs region by month. Finance needs the national total by quarter. If each level is forecast separately, the numbers won’t add up: SKUs might sum to 9,500 while the national forecast says 10,000. Forecasts that add up across the hierarchy are called coherent.

There are four main ways to get there:

• Bottom-up: forecast every SKU and add them up. It keeps local detail, but SKU-level data is noisy, so the totals can drift.
• Top-down: forecast the total, which is smoother and easier to predict, then split it down using historical proportions. It’s stable but loses local patterns, such as one region growing faster than others.
• Middle-out: forecast at a middle level, say product family by region, then aggregate up and split down from there.
• Reconciliation (for example MinT): forecast every level, then adjust all of them together into a coherent set, trusting each level according to how reliable its forecasts have been. Done well, this can be more accurate than any single level on its own.

The hierarchy usually runs in several directions at once: product (category, brand, SKU), geography (country, region, warehouse) and time (week, month, quarter).

The example

Three SKUs of a shampoo brand. Forecasting each SKU and the brand total separately gives numbers that don’t add up:

Bottom-up: keep the SKU forecasts and set the total to 9,500. Simple and detailed, but it ignores the total forecast, which is often the more reliable one.

Top-down: keep the total of 10,000 and split it by historical shares. If A, B and C historically sold 50%, 30% and 20%, they become 5,000, 3,000 and 2,000. C jumps from 1,500 to 2,000, losing the information that C has been declining.

Shares can be chosen several ways: the average of historical proportions, the proportion of historical averages, or shares taken from the lower-level forecasts themselves (forecast proportions), which keep recent shifts in the mix.

Reconciliation

Reconciliation forecasts every level, then adjusts all the forecasts together, as little as possible, until they add up. The simplest version (OLS reconciliation) spreads the gap equally across every node of the hierarchy. Here the gap is 10,000 − 9,500 = 500 across four nodes (three SKUs and the total), so each moves by 125: the SKUs up and the total down.

The numbers now add up, and every level’s information has been used. MinT (minimum trace) does the same but weights the adjustments by how reliable each forecast has been: if the brand total has historically been much more accurate, it moves less and the SKUs absorb more of the gap.

Choosing an approach

• A strong, stable signal at the bottom: bottom-up.
• A noisy bottom with a stable mix: top-down or middle-out.
• Data and tools available: reconcile, which often improves accuracy at every level.

Hierarchies in several directions

Real hierarchies are grouped: the same sales add up by product (SKU, brand, category), by geography (store, region, country) and by channel, and every path must agree. Temporal hierarchies add time: weekly forecasts should add up to the monthly and quarterly ones. Reconciling across time can improve accuracy too, because annual patterns are clearer in monthly data and short-term shifts are clearer in weekly data.

Why reconciliation can improve accuracy

Each level sees the data differently: the total is smooth and shows trend and seasonality clearly, while the bottom shows mix shifts and local events. Reconciliation combines these views, much as averaging several forecasts beats picking one. The MinT approach (Wickramasuriya, Athanasopoulos and Hyndman, 2019) chooses the combination that minimizes the total variance of the reconciled forecast errors, given how the base forecast errors vary and move together.

Practical problems at scale

• Size: SKU × store × day can mean millions of bottom-level series, so full reconciliation needs efficient methods or a reduced hierarchy.
• Negative forecasts: adjustments can push small items below zero; constrained methods prevent this.
• Intermittent bottoms: at SKU-store-day level most values are zero, so forecasting higher up and splitting down is often more stable.
• Manual changes: when sales changes a regional total, the system must push that change down consistently. Planning tools do this with disaggregation rules, proportional to forecast, history or another key.

One number, many views

Reconciled forecasts are the basis of “one number” planning. Finance’s revenue view, sales’ customer view and supply’s SKU-location view all come from the same coherent set, converted into units, value or capacity as needed. Sales and operations planning can then work at family level for volume and at SKU level for mix, without the two drifting apart.