Pricing Structural Restrictions in Time-Series Forecasting

The same architectural choice can improve some time-series predictions and worsen others. We examine this variation by comparing the predictive cost of structural restrictions with the learning cost they can save. Here, learning cost is the prediction loss above a structure's best attainable performance due to imperfect estimation and optimization with limited data and resources. In linear prediction settings, we express structural restriction costs through properties of the data distribution, termed data requirements. An orthogonal-design ridge comparison then identifies when estimation savings outweigh the cost of restricting inputs. These results motivate held-out comparisons of restricted linear reference predictors to estimate selected data requirements. In controlled experiments, larger measured requirements tend to accompany larger gains from relaxing the corresponding restriction. Combining these measurements with candidate configurations and a finite-sample approximation to the estimation component of learning cost yields recommendations without training candidates or using performance results from other datasets. Across ten forecasters and 14 datasets, the three recommended candidates have a mean excess test error of 5.9% over the best candidate overall, comparable to the strongest training-free proxy (6.8%) and selectors trained on other datasets.