Dealing with idiosyncratic cross-correlation when constructing confidence regions for PC factors

TL;DR

This paper introduces a simple, adaptive thresholding estimator for the asymptotic covariance matrix of Principal Components factors, effectively handling cross-correlated idiosyncratic components and outperforming existing methods.

Contribution

It proposes a novel, computationally simple estimator for the covariance matrix of PC factors that accounts for cross-correlated idiosyncratic errors, improving confidence region accuracy.

Findings

Estimator outperforms existing methods in simulations

Effective in various cross-correlation structures

Provides more accurate confidence regions

Abstract

In this paper, we propose a computationally simple estimator of the asymptotic covariance matrix of the Principal Components (PC) factors valid in the presence of cross-correlated idiosyncratic components. The proposed estimator of the asymptotic Mean Square Error (MSE) of PC factors is based on adaptive thresholding the sample covariances of the id iosyncratic residuals with the threshold based on their individual variances. We compare the nite sample performance of condence regions for the PC factors obtained using the proposed asymptotic MSE with those of available extant asymptotic and bootstrap regions and show that the former beats all alternative procedures for a wide variety of idiosyncratic cross-correlation structures.