Cross-Window Relations for Transferability Estimation in Time Series Forecasting

Time series forecasting often benefits from transferring knowledge from auxiliary datasets, yet transfer performance depends strongly on which source dataset is selected. Existing transferability estimators mainly assess source–target compatibility at the level of individual forecasting windows, overlooking the local evolution between successive overlapping windows. In this paper, we introduce the Cross-Window Relation Estimator (CWRE) for source dataset selection in time series forecasting. CWRE evaluates each candidate source using its frozen source-pretrained model on the target dataset, jointly measuring how well the learned representations explain future sequences and how well representation changes explain the corresponding future changes across adjacent windows. To reduce noise amplification introduced by differencing, CWRE separates trend and seasonal components, applying cross-window evaluation to the smoother trend component while retaining complementary predictive information through instance-wise evaluation. These relations are integrated through closed-form ridge regression, enabling efficient scoring without target-domain fine-tuning. We further evaluate transferability under a cross-architecture protocol, where scoring and downstream forecasting models are distinct. Experiments across multiple target datasets, architectures, and missing-observation settings show that CWRE achieves higher overall agreement with downstream transfer-performance rankings than distribution-alignment, task-transferability, and time-series-specific baselines. The results demonstrate that cross-window evolution provides complementary information for identifying transferable source datasets beyond conventional instance-wise compatibility. To ease reproducibility, we release our implementation code online https://anonymous.4open.science/r/CWRE-submission-3FC1/.