Quantifying Protocol-Induced Uncertainty in Comparative Predictive-Model Evaluation: Evidence from Large-Scale Daily PM10 Forecasting

(a) Many air quality forecasting studies report gains from machine learning, but evaluations often use static chronological splits and omit persistence baselines, so the operational added value under routine updating is unclear. (b) Using 2,350 daily PM10 observations from 2017 to 2024 at an urban background monitoring station in southern Europe, we compare XGBoost and SARIMA against persistence under a static split and a rolling-origin protocol with monthly updates. We report horizon-specific skill and the predictability horizon, defined as the maximum horizon with positive persistence-relative skill. Static evaluation suggests XGBoost performs well from one to seven days ahead, but rolling-origin evaluation reverses rankings: XGBoost is not consistently better than persistence at short and intermediate horizons, whereas SARIMA remains positively skilled across the full range. (c) For researchers, static splits can overstate operational usefulness and change rankings. For practitioners, rolling-origin, persistence-referenced skill profiles show which methods stay reliable at each lead time.

A forecasting benchmark reports which method won. We show that the answer is set by the evaluator's choices before any model is fitted. We benchmark 24 forecasting methods and one textbook reference, including six 2025-era time series foundation models, on a production marketplace panel of 1,887 business customers over 67 months. We hold the data, the horizon and the period fixed, and vary only the evaluation design. Three choices each reverse or dissolve a headline conclusion. Changing the unit of analysis from the market total to the individual customer moves our production baseline from second of nineteen, beaten by nothing, to twenty-third of twenty-five. Nineteen of its twenty-four challengers beat it there. Changing how much error is pooled decides whether a Diebold-Mariano test finds anything at all. Scoring prediction intervals rather than point forecasts reorders the field almost completely, with a rank correlation of 0.02 on intermittent demand. We then measure what the deployed system gets from this. Its selection rule captures 55% of the distance between doing nothing and choosing with hindsight. The reversal is not a quirk of our data. We ran the released protocol, unchanged, on the public M5 retail panel. The same baseline shape places first at the market total and last per series, beaten by everything, and a replayed selection rule closes 64.7% of the same floor-to-ceiling distance there. Adding five zero-shot foundation models to that roster changes who wins at the total, not the shape. The bands' blind spot travels too: conformal bands under-cover most on the spikiest items. Splitting our own panel into ever smaller groups turns the contrast into a curve: the baseline's rank worsens at every level of disaggregation. We release the evaluation protocol and report an error of our own that inverted a result before we caught it.

We study the problem of model selection among probabilistic forecasting models evaluated on datasets of multiple time series. The performance of a model on a single time series is quantified by the average value (score) of a proper scoring rule over a test set, but extending model selection to data sets of time series requires aggregating these scores. Common approaches either rely on scaling scores and averaging them (mean scaled score) or avoid scaling by using alternative statistics such as mean ranks or win rates. However, these approaches can yield conflicting conclusions. We show that such discrepancies arise from the skewness of the distribution of the scores, which is particularly pronounced when test sets are short. The skewness can cause non-mean criteria (e.g., mean rank, median, win rate) to select misspecified models. In contrast, the mean score is immune from this problem. We further show that, as the size of the test sets increases, all aggregation criteria converge to the same model selection decision, mitigating these discrepancies. Our experiments on intermittent demand time series, including data from the M5 competition, highlight the importance of sufficiently large test sets; the mean scaled score appears to be the more reliable approach, also because empirically we found its decision to remain consistent when different scaling factors are adopted.