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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.

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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., 26 Jan 2024) in Section 3.4 (High-dimensional variable selection in presence of parameter instability)