Resumen de Measuring uncertainty of factors extracted using principal components
Javier de Vicente Maldonado
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. However, in this thesis, we show that the asymptotic distribution of PC factors could not be an appropriate approximation to the finite sample distribution for the sample sizes and cross-sectional dimensions usually encountered in practice. The main problem is that parameter uncertainty is not taken into account.
In the second chapter of this thesis, we show that neither the asymptotic distribution nor several bootstrap procedures with goals related to inference proposed in the context of DFMs are appropriate to measure the uncertainty of PC factor estimates. Therefore, we propose a subsampling procedure designed for this purpose. The 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.
In chapter 3, the GiS (Growth-in-Stress), a new macroeconomic risk index, is proposed. The methodology for constructing the GiS is based on predictive quantile factor regressions. The factors are extracted using principal components (PC) and their joint probability density is obtained using the subsampling method proposed in the second chapter. To construct the risk index, we follow the Value-in-Stress (ViS) risk measure proposed by González-Rivera (2003). The GiS calculates the risk exposure to stressed scenarios and the country's ability to withstand them.
Finally, chapter 4 concludes and presents the lines of research currently being undertaken.
