Global Models Versus Local Models
Why fitting one model across thousands of series beats fitting one model per series, what cross-learning provides that per-series estimation cannot, and where local models still win.
Classical forecasting fits a model to a series: estimate ARIMA parameters for this product's sales, another set for that one. With ten series that is reasonable. With half a million SKUs it is both computationally awkward and statistically wasteful, because each model sees only its own history and learns nothing from the thousands of similar series beside it.
A global model is one model fitted across all series, taking the series identity and its features as input. The shift from local to global is the single largest change in practical forecasting over the past decade, and it is what let machine learning methods overtake statistical ones on large-scale problems.
What cross-learning buys
Short series become forecastable. A product with six weeks of history cannot support a seasonal model estimated from its own data. A global model has learned seasonal shapes from thousands of similar products and applies them, which is the difference between a forecast and a guess.
Rare patterns are learned once. Promotional spikes, holiday effects and stockout depressions occur rarely in any single series and frequently across the population. Only a global model accumulates enough examples to learn them.
Cold start is a prediction rather than a special case. A new item with covariates similar to existing items inherits their behaviour, so it can be forecast on day one.
Regularisation is implicit. Sharing parameters across series constrains each one, which reduces the overfitting that plagues per-series estimation on short noisy histories.
The empirical support is strong: global methods, gradient-boosted trees on lag features and neural sequence models alike, have dominated recent large-scale forecasting competitions, where the winning entries have consistently been global rather than per-series.
Where local still wins
Few series with long histories and idiosyncratic dynamics. A handful of national aggregate series, each with fifteen years of data and its own structural breaks, gives per-series estimation enough data and gives cross-learning nothing to learn from. Global models need many series to be worth the machinery.
Local models are also interpretable in a way global ones are not: an ARIMA specification says something about the series, whereas a global model's parameters describe the population.
When it breaks
Heterogeneous scale distorts training. Series spanning six orders of magnitude in volume make the loss dominated by the large ones, so small series are fitted badly. Per-series normalisation before fitting, and denormalisation after, is not optional.
The series identifier can be memorised. Given a high-cardinality series ID as a feature, the model can fit each series individually and lose the cross-learning that motivated the approach. Regularising the embedding or omitting the ID in favour of descriptive features is what preserves sharing.
One model implies one set of assumptions. A global model applies the same functional form to intermittent demand, smooth seasonal series and trending series alike. Segmenting into a few global models by pattern type frequently beats one global model over everything.
Debugging is harder. When a single series forecasts badly, there is no per-series model to inspect, and the cause may be in data preparation, in the population's influence, or in that series' features. This is a real operational cost of the approach.
12 flashcards for this concept
Click a card to reveal the answer.