Forecasting by style, colour, size and store: hierarchies explained

KEY TAKEAWAYS Summary by the editors

1. Fashion data forms hierarchies (for example department, style, colour, size) and cross-cutting groupings (for example region, store, channel), and forecasts made separately at each level will usually not add up.
2. Coherence means forecasts sum consistently: size forecasts add to colour forecasts, which add to style forecasts, which add to the total.
3. Bottom-up forecasting keeps only the lowest level and sums upwards, top-down splits a total using proportions, and middle-out starts at an intermediate level and goes both ways.
4. According to the Hyndman and Athanasopoulos textbook, no top-down method satisfies the unbiasedness condition, so top-down approaches yield biased coherent forecasts.
5. Optimal reconciliation (MinT) adjusts independent forecasts from all levels so that they add up, and its authors report that reconciled forecasts are at least as good as the incoherent base forecasts.

Hierarchical forecasting is the practice of forecasting demand at several levels, such as total, style, colour, size and store, and then making those forecasts consistent with each other. It matters in fashion because buying decisions are made at the style level, allocation at the size and store level, and financial plans at the total level, and these views must agree.

This explainer sets out how the structure arises, the classic approaches, the idea of reconciliation, and the data issues specific to fashion.

What is a hierarchy in fashion forecasting?

A hierarchical time series arises when attributes are nested. Hyndman and Athanasopoulos, in their open textbook Forecasting: Principles and Practice, give the example of country, state, region and outlet. In fashion the nesting is typically department, category, style, colour and size. A grouped series arises when attributes are crossed rather than nested, such as size, gender and price range, which do not break down in one unique order. Real fashion data is usually mixed: product levels are nested, while store, region and channel cut across them.

The structure matters because each level answers a different question. A buyer needs a style forecast, a planner needs the size curve, and a store allocator needs store-level numbers. The textbook calls the central problem coherence: forecasts should add up the same way the data does, so that regional forecasts sum to national forecasts.

Why do forecasts at different levels not add up?

If each series is forecast on its own, the results usually do not sum. A style forecast produced from style-level history will differ from the sum of its size forecasts, because each model sees different noise and different patterns. The textbook states the cause directly: base forecasts for each series are produced independently, so they usually do not satisfy the aggregation constraints.

This is not just a presentation problem. If purchasing follows the style forecast and allocation follows the size forecast, the company will buy one number and distribute another. Inconsistent forecasts also make it hard to trace why a plan was missed.

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What are bottom-up, top-down and middle-out approaches?

The textbook describes three traditional approaches, all based on forecasts from a single level.

• Bottom-up: keeps only the lowest-level base forecasts and sums them upwards. Higher-level forecasts are discarded. It keeps local detail but inherits the noise of sparse series such as size by store.
• Top-down: splits a top-level forecast into lower levels using proportions, then sums back up. It is stable at the top but loses local signals. The textbook states that no top-down method satisfies the unbiasedness condition, so all top-down approaches yield biased coherent forecasts.
• Middle-out: chooses an intermediate level, such as style, disaggregates it downwards and sums it upwards. It is a common compromise in fashion, where style is the natural planning unit.

These methods use information from only one level and discard the rest, which is the motivation for reconciliation methods.

How does forecast reconciliation work?

Reconciliation takes base forecasts from every level, produced by any method, and adjusts them so that they are coherent. The textbook writes this as a linear mapping from base forecasts to bottom-level forecasts, which are then summed through the hierarchy. The best-known optimal method is MinT, short for minimum trace, which chooses the mapping that minimises the sum of the variances of the coherent forecast errors, subject to a condition that keeps unbiased forecasts unbiased.

MinT was proposed by Wickramasuriya, Athanasopoulos and Hyndman in a Monash University working paper dated 2017 and revised in January 2018. The authors show that the covariance matrix of the earlier generalised least squares method cannot be estimated in practice, propose a workable alternative, and state that MinT reconciled forecasts are at least as good as the incoherent base forecasts. In their simulations and an Australian tourism application, the shrinkage-based variant generally performed best.

The textbook lists simpler approximations when the error covariance is hard to estimate: ordinary least squares, weighted least squares scaled by residual variances, weighted least squares based only on the structure (useful when residuals are unavailable, as with judgmental forecasts), and a shrinkage estimator for cases with many bottom-level series relative to the series length. It also notes that reconciliation can reveal patterns that aggregation hides, such as contrasting regional seasonal patterns smoothed out at the national level.

What are the data problems specific to fashion?

A position paper on learning-based forecasting in fashion, by researchers at the University of Verona and Humatics, argues that clothing's short life cycle makes restocking difficult and that classical methods such as ARIMA cannot be fitted when there is no history or only a few observations. The paper focuses on new product forecasting rather than hierarchies, but it explains why the style level in fashion is often the hardest one to forecast from its own history.

• New styles have no history, so forecasts borrow from similar styles, attributes or early sales.
• Size and store series contain many zeros, which makes percentage errors unstable and low-level models noisy.
• Master data changes, such as a style being recoloured or a store closing, break the hierarchy over time.
• Wholesale-led brands may only see sell-in at customer level, not sell-out at store level, so the lower levels are partly invisible.

Read also

What is size curve optimisation and how does AI help buy the right sizes?

How should a team start?

1. Write down the hierarchy and the decision made at each level.
2. Choose the planning level that is stable enough to forecast, often style or style-colour.
3. Forecast the levels you can, using simple benchmarks as a reference.
4. Reconcile, and compare reconciled against unreconciled forecasts on a hold-out period.
5. Review where reconciliation changes numbers most: those are usually data problems, not model problems.

Hierarchical forecasting is therefore less a single technique than a discipline: decide which levels matter, forecast what the data supports, and make the numbers add up in a way that can be explained to buyers and planners.

Frequently asked questions

What is hierarchical forecasting?

It is forecasting at several levels of a structure, such as total, style, colour, size and store, and making the forecasts consistent. The aim is that lower-level forecasts sum to higher-level ones, which is called coherence.

What is the difference between bottom-up and top-down forecasting?

Bottom-up forecasts the lowest level and sums upwards, so it keeps detail but inherits noise. Top-down forecasts a total and splits it by proportions. The Hyndman and Athanasopoulos textbook states that no top-down method satisfies the unbiasedness condition.

What is MinT reconciliation?

MinT, or minimum trace, is a method that adjusts forecasts from all levels so they add up while minimising the variance of the reconciled errors. Its authors state that the reconciled forecasts are at least as good as the incoherent base forecasts.

Why is size-level forecasting so difficult in fashion?

Size series are sparse, with many zeros and strong noise, and styles live only for a season. Models therefore often forecast a higher level and distribute to sizes using a size curve, then check the result with reconciliation.

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