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Title: Measuring the uncertainty of principal components in dynamic factor models Authors:  Esther Ruiz - Universidad Carlos III de Madrid (Spain) [presenting]
Irene Albarran - Universidad Carlos III de Madrid (Spain)
Javier de Vicente - Universidad Carlos III de Madrid (Spain)
Abstract: Factors extracted from large macroeconomic are central for policy makers. Measuring the uncertainty associated with the estimated factors is a central issue for an adequate policy. One of the most popular factor extraction procedures is Principal Components which is nonparametric and computationally simple. The uncertainty associated with factors extracted using PC can be measured using their asymptotic distribution. However, the asymptotic distribution is a poor approximation to the finite sample distribution of the factors. The asymptotic intervals are too tiny. Alternatively, several authors propose using bootstrap methods in the context of PC factor extraction. We show that the available bootstrap methods are not adequate as they are based on bootstrapping the data as if it were iid, on bootstrapping from the marginal instead of the conditional distribution or on considering the estimated common component as if it were the true component. After a detailed analysis of the finite sample properties of the asymptotic and bootstrap factor prediction intervals, we propose a new bootstrap procedure with appropriate properties that mimic that of the original data. We show that the coverages of the new bootstrap intervals are close to the nominal regardless of the properties of the idiosyncratic noises as far as the factor is not close to the nonstationary region.