Budgeted Temporal Context Selection for Time Series Forecasting

Time series forecasters may have access to long histories while being able to process limited number of observations. We study how this fixed temporal budget should be allocated over the available history. We define layout quality through conditional prediction risk and start analysis through a local linear trend model, where the risk is available exactly. With two observations, historical separation improves estimation of the current trend, while drift makes sufficiently old observations stale, this tradeoff yields an optimal historical separation. For larger budgets, optimization over 189 settings finds an exact recent--historical two-block optimum in $89.9$% of cases, with at most $0.099$% excess risk otherwise. For unknown processes, we retain the same covariance-based prediction criterion and estimate it directly from training data. On synthetic local linear trend data, a shared lag-aware Transformer closely follows the analytical layout landscape, with mean Pearson correlation $0.990$ for predicted and realized gains and median Spearman correlation $0.889$ across candidate layouts. On ETT, the empirical score predicts layout quality for linear, MLP, and Transformer forecasters, with broadly aligned rankings across model classes. The benefit of temporal allocation is largest under small observation budgets. Overall, these results show that context size and context placement are distinct design choices in forecasting under limited temporal capacity.