Forecasting at Scale: Global, Probabilistic & Hierarchical Models
Forecasting a million series coherently, with quantiles, intermittency and backtests that do not lie
Take forecasting from one series to a million: why one global model trained across series beats per-series models once histories are short (a 100-series simulation where the per-series boosted model scored MASE 0.995 and a pooled model on 1,000 series scored 0.862), global LightGBM panels with lags, calendar, promo and price features, target scaling (raw targets lost 17 points of WAPE on the smallest-scale quintile), and direct versus recursive versus window horizons (a 14-model direct set, one window model and a recursive loop landed within 1.3 percent of each other). Then deep forecasters (N-BEATS and N-HiTS, DeepAR, Temporal Fusion Transformer, PatchTST) and time-series foundation models (TimesFM, Chronos, Moirai) with an honest account of when they beat boosting and why their benchmarks can leak; probabilistic forecasting with pinball loss, CRPS and coverage (quantile GBM covered 79.5 percent of an 80 percent interval, an in-sample residual band only 73.2); intermittent demand with Croston, SBA, TSB and Tweedie, where an all-zeros forecast won MAE by 30 percent and the metric choice flipped the winner three times; hierarchical and grouped forecasting with coherence, bottom-up, top-down, middle-out, OLS, WLS and MinT reconciliation, temporal hierarchies, and a 7-series worked example with the S matrix and the full MinT arithmetic; evaluation at scale with rolling-origin backtests, MASE, RMSSE, WAPE, pooled versus per-series aggregation and forecast value added; known-future inputs and price elasticity (an endogenous price turned a true elasticity of -1.5 into +0.38); and production concerns from retraining cadence to forecast overrides. Every number comes from code that was run.
Practice questions (6)
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Design the feature set for a global daily demand model over 400,000 SKU-store pairs
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Choose between direct, recursive and single-model horizon strategies for a 28-day forecast
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Reconcile forecasts for a company, two regions and four stores
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Pick the metric and method for 80,000 slow-moving spare-part SKUs
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Build a leakage-free backtest for a weekly retail forecasting model
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