Inferential Theory for Factor Models of Large Dimensions

This paper develops an inferential theory for factor models of large dimensions. The principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator (if normality is assumed). We derive the rate of convergence and the limiting distributions of the estimated factors, factor loadings, and common components. The theory is developed within the framework of large cross sections ("N") and a large time dimension ("T"), to which classical factor analysis does not apply.We show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of "N" and "T". The estimated factors…