Choosing estimation windows or weights under parameter instability

Develop a generally applicable procedure for selecting estimation window lengths and/or observation weighting schemes for high-dimensional time-series forecasting when parameters are unstable or subject to structural breaks, ensuring reliable inference and prediction.

Background

Forecasting in the presence of parameter instability requires decisions about how much historical data to use and how to weight it. The authors discuss continuous versus discrete structural breaks and the implications for optimal weighting, referencing related work on robust weights.

Despite these discussions, there is no fully satisfactory, broadly applicable procedure to determine windows or weights in practice, leaving a key methodological issue unresolved for high-dimensional forecasting applications.

References

Determining the appropriate window or weighting for the observations before estimation is a difficult problem and no fully satisfactory procedure seems to be available.

— High-dimensional forecasting with known knowns and known unknowns  (2401.14582 - Pesaran et al., 2024) in Section 3.4 (High-dimensional variable selection in presence of parameter instability)

Our sensitivity analysis shows that performance depends materially on these choices, and the development of principled, data-adaptive parameter selection remains an open problem.

— Mixup Barcodes for Topology-Aware Financial Decision Making  (2610.12396 - Sharma et al., 8 Oct 2026) in Section 6.1, “Limitations”

Besides, gains on historical windows do not guarantee gains on future forecasts. This highlights the open problem, i.e., distribution shift, in time-series forecasting \citep{pmlr-v235-liu24ae,Kim2025}.

— TIMERSI: Towards Self-Improved Agentic Deployment for Time-Series Foundation Models  (2610.19725 - Liu et al., 14 Oct 2026) in Limitations section