A0178
Title: Dealing with idiosyncratic cross-correlation when constructing confidence regions for PC factors
Authors: Esther Ruiz - Universidad Carlos III de Madrid (Spain) [presenting]
Diego Fresoli - Vienna University of Technology (Austria)
Pilar Poncela - Universidad Autonoma de Madrid (Spain)
Abstract: The finite sample performance of asymptotic and bootstrap regions is analysed for PC factors. It is shown that when the idiosyncratic components are wrongly assumed to be cross-sectionally uncorrelated, prediction regions for the estimated factors based on standard asymptotic results can have wrong coverages, which can be either larger or smaller than the nominal depending on the covariances of the idiosyncratic noises and the factor loadings. Procedures to compute the asymptotic MSE of the factors, taking into account the idiosyncratic cross-dependence, can help but are still inadequate depending on the structure of the cross-correlations. It is also shown that alternative extant bootstrap procedures may also have wrong coverages in front of realistic idiosyncratic correlations. Alternatively, a computationally simple estimator of the asymptotic covariance matrix of the factors is proposed based on adaptive thresholding of the sample covariances of the idiosyncratic residuals with the threshold based on the variance of each individual entry of the sample covariances.
