spb/wp23_uqo

1\section{Empirical forecasting framework}\label{sec:framework}23Forecasts are produced in forward-chaining fashion. For Task~A, twelve quarterly origins (December 2022 to September 2025) each yield a training set of all sales dated $\le o$ (with horizon-dated features) and a test set of the sales of the following twelve months; for Task~B, the models are re-estimated at every third origin on the rows whose targets were observed by the origin and used for the next three origins, which gives 34 to 45 evaluated origins per horizon. Point accuracy is reported as MAE, RMSE, median absolute error, bias and MASE relative to the naive reference; probabilistic accuracy as the mean pinball loss, the quantile-grid CRPS, 50\% and 90\% coverage and widths and the weighted interval score. Statistical comparisons use per-origin mean losses (which removes the cross-sectional dependence among forecasts issued at the same origin and leaves a short time series of $n$ origins): the Diebold--Mariano test with a Newey--West long-run variance with $h-1$ lags and the Harvey--Leybourne--Newbold small-sample correction, the Giacomini--White conditional test with a constant and the lagged loss difference as instruments, stationary-bootstrap confidence intervals for mean loss differences, and the model confidence set at the 10\% level with the $T_{\max}$ statistic and 500 bootstrap replications. With 34 to 45 origins these tests have limited power and are interpreted with the economic magnitudes alongside. Heterogeneity is reported by level, class, region, municipal size and price segment, and never for cells with fewer than 30 evaluated forecasts.4