Title: Resampling uncertainty of principal components factors
Authors: Javier de Vicente Maldonado - Carlos III University (Spain) [presenting]
Esther Ruiz - Universidad Carlos III de Madrid (Spain)
Abstract: In the context of Dynamic Factor Models (DFMs), one of the most popular procedures for factor extraction is Principal Components (PC). Measuring the uncertainty associated to PC factor estimates should be part of interpreting them. Although the asymptotic distribution of PC factors is known, it could not be an appropriate approximation to the finite sample one for the sample sizes and cross-sectional dimensions usually encountered in practice. The main problem is that it does not take into account parameter uncertainty. Alternatively, several bootstrap procedures have been proposed in DFM with goals related to inference. We show that these procedures are not appropriate to measure the uncertainty of PC factor estimates and propose an alternative resampling procedure designed with this purpose. The asymptotic and finite sample properties of the proposed procedure are analyzed and compared with those of the asymptotic and alternative extant bootstrap procedures. The results are empirically illustrated obtaining confidence intervals of the underlying factor in a system of Spanish macroeconomic variables.