Accurate Confidence Regions for Principal Components Factors

In dynamic factor models, factors are often extracted using principal components with their asymptotic confidence regions having empirical coverages below the nominal ones when the temporal dimension is small. We propose a subsampling procedure to compute the factor loadings uncertainty and correct the asymptotic covariance matrix of the extracted factors. We show that the empirical coverages of the modified confidence regions are closer to the nominal ones than those of asymptotic regions and asymptotically valid bootstrap regions. The results are empirically illustrated obtaining confidence intervals of the underlying factor in a system of Spanish macroeconomic variables.