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 $0<\alpha _{k}\leq 1$ for $k=1,2,...,r$. We establish the asymptotic validity of our bootstrap method using not only the conventional data-dependent rotation matrix $\hat{\bH}$, but also an alternative data-dependent rotation matrix, $\hat{\bH}_q$, 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 ${\bH}$, which is unique and can be regarded as the population analogue of both $\hat{\bH}$ and $\hat{\bH}_q$. Experimental results provide compelling evidence that the proposed bootstrap procedure achieves superior performance relative to the existing procedure.