Demand forecasting under high volatility: a design for multi-region commerce

1Context and motivation

Many commerce decisions rest on a demand forecast: how much stock to buy and where to place it, how much safety stock to hold, how hard to push a promotion, which delivery promise to show, and what carrier capacity to book. Errors during a sales event, a promotion or a sudden rise in interest in one product matter most, because that is when stock-outs and overstock are largest.

Classical forecasting treats a series as trend, seasonality and noise. That decomposition works well when the series is long, regular and slowly changing. Commerce demand often is not. Sales events and promotions are dense and overlap; prices and discounts change; new products have no history; currency and payment conditions differ between regions; and some products sell a few units a week while others sell thousands. A single model family tuned for one of these conditions tends to fail on the others.

This paper describes the forecasting architecture we propose for that setting. Its unit is a product at a store or location in a region, at daily resolution, with an hourly path for a small set of high-volume products. We describe the design and the reasons for each part of it. We do not report accuracy results, because we have not run the evaluation that would produce them.

2Background

2.1Classical models

Autoregressive integrated moving average models, with their seasonal extension, describe a series through its own lags and lagged errors after differencing, and come with a full procedure for identification, estimation and diagnostic checking¹. Exponential smoothing, including the Holt-Winters method with trend and seasonal components, weights recent observations more heavily than older ones². Both are fitted series by series and are cheap, but a model fitted to one short series cannot borrow from thousands of similar series, and an event that has never appeared in that series cannot be anticipated.

2.2Global and probabilistic deep models

DeepAR trains one autoregressive recurrent network on a large number of related series and produces a full predictive distribution rather than a single value; its authors motivate it with retail demand, where the right quantity of stock in the right place depends on the distribution, not the mean³. N-BEATS uses a deep stack of fully connected layers with backward and forward residual links; it was evaluated on the M3, M4 and TOURISM competition datasets, and a variant of it produces interpretable outputs⁴. Both are global models: parameters are shared across series, which is what lets a new or sparse series draw on the others.

2.3Attention-based models

The Temporal Fusion Transformer handles the mix of inputs that commerce forecasting has: static covariates such as product category, inputs known in advance such as a planned promotion or a holiday, and inputs observed only in the past such as page views. It uses recurrent layers for local patterns, interpretable self-attention for long-range dependencies, and gating and variable-selection components to suppress inputs that do not help⁵. A line of work adapts attention to long horizons. Informer reduces the cost of self-attention on long sequences⁶; Autoformer makes series decomposition an inner block of the model and replaces point-wise attention with an auto-correlation mechanism⁷; PatchTST splits each series into patches that serve as input tokens and shares weights across series⁸.

2.4The case against assuming attention helps

The evidence on Transformers for forecasting is not one-sided. On nine real datasets, a set of one-layer linear models outperformed the Transformer-based long-horizon models of that time in every case, often by a large margin; the authors argue that permutation-invariant self-attention loses temporal ordering information⁹. We take this as a design constraint, not a footnote: no model family is adopted for a segment unless it beats simple and classical baselines on that segment under the same protocol.

2.5Retail hierarchies

Commerce forecasts are needed at several levels at once: product, category, store, region. The M5 competition set the task in this form, asking for forecasts of 42,840 hierarchical unit-sales series from Walmart, with forecasts at the lowest level summed upward to the other levels¹⁰. When each level is forecast separately, the forecasts do not add up. Reconciliation adjusts them so that they are coherent². The trace minimisation method uses the full covariance matrix of forecast errors and minimises the mean squared error of the coherent forecasts across the whole collection, assuming unbiased base forecasts, with a closed-form solution¹¹.

3What the design must handle

We set six requirements from the setting described above. They are design choices, not findings.

• Regime changes. Large deviations during events are often the most important points for the business, so the design must model them as signal with explicit event inputs rather than discard them as outliers.
• Heterogeneity across regions. Regions differ in event calendars, currencies and payment conditions. The design lets the model learn region-specific effects rather than assume one seasonal profile.
• Exogenous inputs. Promotions, prices, holidays, stock-outs and supply constraints enter as covariates, not as unexplained noise.
• Uncertainty. Inventory decisions need quantiles, so every model in the stack produces a predictive distribution or a set of quantiles.
• Operator trust. A planner has to see which inputs moved the forecast.
• Cost and latency. Nightly forecasts cover many series; the intra-day path covers few, and the compute budget for each is fixed in advance.

4Architecture

The stack has five layers.

4.1Data and signal layer

The grain is product by store or location by region by day, with an hourly grain for a small set of high-volume products. Inputs are orders, views, add-to-cart events, cancellations, returns, stock-outs, prices, discounts and promotions. Exogenous inputs are holidays and planned sales events, logistics constraints, and macroeconomic indicators where they are available for the region.

Sales recorded while an item was out of stock understate demand, so the design flags those periods to keep the model from learning the constraint as a fall in demand.

4.2Feature and embedding layer

Each region and product receives a learned embedding, combined with calendar features (day of week, week of year) and event indicators. The region embedding is where differences in seasonality and response to promotions are absorbed. Inputs are labelled by type, static, known in advance, or observed only in the past, because the attention-based models treat these types differently⁵.

4.3Model layer

Three families run side by side and compete per segment.

• Classical baselines: seasonal naive, exponential smoothing and seasonal ARIMA^{2, 1}, plus a linear model of the kind shown to be a strong baseline for long horizons⁹.
• Global deep models: DeepAR for probabilistic forecasts shared across series³ and N-BEATS for point forecasts with an interpretable configuration⁴.
• Attention-based models: the Temporal Fusion Transformer where rich known-in-advance covariates exist⁵, and a patch-based model for long horizons⁸.

Series are grouped by volatility (rolling variance, promotion density, stock-out frequency), and each group uses the family with the lowest error under the protocol below; a simpler family wins ties.

4.4Reconciliation and calibration layer

Raw forecasts are post-processed in three steps. Negative values are clipped and known capacity limits are applied. Forecasts across the product and location hierarchy are reconciled so that store forecasts sum to the region forecast and product forecasts sum to the category forecast¹¹. Quantiles are recalibrated per region against recent coverage, so that a stated 90 percent interval covers about 90 percent of outcomes in that region and not only on average across all regions.

4.5Serving and monitoring layer

The stack produces nightly batch forecasts and rolling intra-day updates for the high-volume set. Monitoring tracks error and interval coverage by region and volatility group, input pipeline freshness, and the share of series where a fallback model was served. A sustained drop in coverage in one region triggers retraining for that region.

5Components and evidence

Table 1 maps each design component to the problem it addresses and the published work it rests on.

Component	Problem it addresses	Evidence
Global model trained across related series	Short or new series have too little history alone	3, 4
Probabilistic outputs and quantiles	Stock decisions depend on the distribution, not the mean	3
Typed covariates (static, known, observed)	Promotions and holidays are known in advance and must be used	5
Patch-based attention for long horizons	Long input windows are costly for point-wise attention	8, 6
Decomposition inside the model	Trend and seasonality obscure longer-range dependencies	7
Linear and classical baselines kept in every comparison	Attention models do not reliably beat simple models	9, 1
Hierarchical reconciliation	Forecasts at different levels do not add up	11, 10
Proper scoring of distributions	Point metrics cannot judge a quantile forecast	12
Scaled error alongside percentage error	Percentage errors break on zero or low volumes	13, 2

Source: our design, with the works cited in the table.

6Evaluation protocol

Before any accuracy claim about this design could be made, it would need the following evaluation.

• Rolling-origin splits. Training and test windows advance through time, and test windows are chosen to include sales events, so that results are not driven by quiet periods only.
• Horizons. Separate scores at 7, 14, 30 and 60 days, because the ranking of model families can change with horizon.
• Point accuracy. Mean absolute error and root mean squared error in units, and mean absolute scaled error for comparisons across series of different scales¹³.
• Distribution accuracy. The continuous ranked probability score, a proper scoring rule that generalises absolute error to a full predictive distribution, plus interval coverage and quantile loss¹².
• Event error. Error restricted to the most volatile tenth of periods, reported separately so that gains in quiet periods cannot hide losses in events.
• Breakdown. Every score by region and volatility group, and at each hierarchy level after reconciliation.
• Baselines. Seasonal naive, exponential smoothing, seasonal ARIMA and a linear model, all on the same splits⁹.

Percentage error is never used alone to choose a model; Table 2 shows why.

7A worked example: percentage error on low volumes

Table 2 takes one hypothetical product over three days, with one quiet day, one ordinary day and one event day, and compares absolute and percentage errors. All demand and forecast values are inputs chosen for illustration.

Day	Actual (units, input)	Forecast (units, input)	Absolute error (units)	Absolute percentage error
Quiet day	2	3	1	50%
Ordinary day	4	5	1	25%
Event day	50	45	5	10%
Mean			2.33	28.3%

Source: Worked model; inputs in the table.

The mean absolute percentage error is driven by the two low-volume days, each off by one unit, while the event day, with five units missing from stock, contributes least. A model tuned to this percentage would trade event-day error for quiet-day error, the opposite of what inventory planning needs. Had the quiet day sold zero units, the percentage error would be undefined; percentage errors are infinite or undefined when an actual value is zero and extreme when it is close to zero². Many common accuracy measures degenerate in such cases, which is why scaled errors were proposed as the standard for comparing accuracy across series¹³.

8Illustrative scenarios

The scenarios below are hypothetical. They show how the layers would interact; they are not results.

A planned sales event. If a merchant planned a multi-day sales event, the event would enter as a known-in-advance input with its dates and discount depth. A model that uses known future inputs would have the information to raise the forecast before the event starts⁵, while a model that sees only past sales would react only after the spike began. The event error in the protocol is the measure that would show whether this happens.

Currency-linked prices. If a product were priced in local currency while its costs moved with another currency, frequent repricing would follow. With price as a covariate and quantile outputs, the forecast could widen its interval when prices change, and restocking could be set from an upper quantile instead of the mean³.

A sudden rise in interest. If a product with little history suddenly drew attention, the global model would have little to go on from that series alone but could draw on similar products through shared parameters. Recent views and add-to-cart events would be the earliest signal. Whether any model family detects the shift earlier than smoothing methods is for the event-error breakdown to show.

9Privacy and fairness

The forecasts run on aggregated series, not on individual shoppers' histories, and personal identifiers are excluded from the inputs.

Systematic under-forecasting in a smaller or more volatile region leads to less stock and longer delivery promises there. Reporting every score by region, and recalibrating quantiles per region, is meant to make such a bias visible rather than averaged away.

Planners see, alongside each forecast, the inputs that moved it most, the attention-based interpretation where the model provides one⁵, and the predictive interval, so that a forecast is read as a range with conditions, not a promise.

10Limitations

• No measurements. We have not run the evaluation protocol. We make no claim that any model family in the stack is more accurate than another on commerce data; every expected benefit is a hypothesis.
• Mixed evidence on attention. Published comparisons disagree on whether Transformer models help forecasting^{9, 8}. Most were run on public benchmarks unlike retail demand, so their rankings may not transfer.
• Data and compute. Global deep and attention-based models need many series and more compute than classical models. Small merchants may have too few series for a model of their own and depend on transfer from shared models.
• Unprecedented shocks. Events with no precedent in the training data are not forecastable from history. Covariates help only for events that someone records.
• Censored demand. Stock-out flags correct for missing sales only as well as stock records are kept. Where they are wrong, the model learns supply limits as demand.
• Operational complexity. Three model families, per-segment selection and reconciliation add monitoring work that we have not costed.
• Long horizons. Uncertainty grows with horizon, and the intervals at 60 days and beyond may be too wide to support decisions in volatile categories.

11Conclusion

We have described a forecasting stack for volatile, multi-region commerce demand: typed event and price covariates, global probabilistic models, attention-based models where their inputs justify them, simple baselines that every model must beat, reconciliation across the hierarchy, and per-region calibration of intervals. Each part rests on published work, summarised in Table 1. What the design lacks is evidence of its own accuracy. The next step is to run the rolling-origin protocol on one region's data, with event error and interval coverage reported alongside point accuracy, and publish what is measured.