An alternative bootstrap procedure for factor-augmented regression models

In this paper, we propose a novel bootstrap algorithm that is more efficient than existing methods for approximating the distribution of the factor-augmented regression estimator for a rotated parameter vector. The regression is augmented by $r$ factors extracted from a large panel of $N$ variables observed over $T$ time periods. We consider general weak factor (WF) models with $r$ signal eigenvalues that may diverge at different rates, $N^{{\alpha }_k}$, where $0<{\alpha }_k\le 1$ for $k=1,2,\mathrm{.}\mathrm{.}\mathrm{.},r$. We establish the asymptotic validity of our bootstrap method using not only the conventional data-dependent rotation matrix $\widehat{\text{bH}}$, but also an alternative data-dependent rotation matrix, ${\widehat{\text{bH}}}_q$, which typically exhibits smaller asymptotic bias and achieves a faster convergence rate. Furthermore, we demonstrate the asymptotic validity of the bootstrap under a purely signal-dependent rotation matrix $\text{bH}$, which is unique and can be regarded as the population analogue of both $\widehat{\text{bH}}$ and ${\widehat{\text{bH}}}_q$. Experimental results provide compelling evidence that the proposed bootstrap procedure achieves superior performance relative to the existing procedure.