Inference with Nonvanishing MIDAS-Weight Estimation Bias

Develop a formal asymptotic treatment of the bootstrap correction for the bias in the nonlinear least-squares estimator of the MIDAS weighting parameters when \(\sqrt{T}/(qN)\to c_0>0\), using an asymptotic framework appropriate to this nonvanishing-bias regime.

Background

The asymptotic normality result for the SsPCA-MIDAS prediction target treats the MIDAS weighting parameters as known. This treatment is justified when T/(qN)→0\sqrt{T}/(qN)\to0, because the nonlinear least-squares estimator then has no first-order asymptotic bias. When T/(qN)→c0>0\sqrt{T}/(qN)\to c_0>0, however, estimating the weighting parameters introduces an asymptotic bias into inference.

A bootstrap correction developed for a related strong-factor factor-MIDAS setting is identified as a possible starting point, but adapting it to SsPCA-MIDAS would require a different asymptotic framework. The unresolved problem is therefore to establish the validity and limiting behavior of such a correction in the weak-factor, supervised-selection setting.

References

When instead \sqrt{T}/(qN)\to c_0>0, the plug-in error induces an asymptotic bias, and the bootstrap correction of could in principle be adapted, though a formal treatment requires a different asymptotic framework and is left for future research.

— Supervised Mixed-Frequency Learning for Macro-Financial Forecasting When Factors are Weak  (2608.12589 - Hounyo et al., 12 Aug 2026) in Remark 1, Section 3, subsection “Inference on the Prediction Target”