Effect of Rolling-Window Forecast Tests Under Structural Instability

Characterize the effect of structural instability in factor loadings and regression coefficients on rolling-window versions of the encompassing test and the Granger-causality test when the predictors are estimated factors.

Background

The paper discusses prior results establishing the asymptotic validity of the encompassing test and the Granger-causality test when factors are estimated recursively. It notes that rolling-window implementations may behave differently when factor loadings and regression coefficients change over time. The unresolved issue concerns the effect of these structural instabilities on the validity or behavior of the corresponding rolling-window tests, which is distinct from the paper’s own analysis of selecting the forecasting-window size.

References

However, when a rolling-window version of these tests is employed, the effect of structural instability in the factor loadings and regression coefficients is unclear.

— Rolling Window Selection in FAR Models with Structural Instabilities  (2610.12025 - Djogbenou, 8 Oct 2026) in Section 1, Introduction