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