Heavy Factor Models: Identification and Estimation via PCA
Authors: Jihyun Kim, Nour Meddahi
Abstract: This paper considers a factor model with heavy factors that have potentially unbounded variance. For the factor model, we revisit the validity of the PCA based identification and estimation methods. Under the unbounded variance, the usual L2-projection based methods, such as the PCA, are not well defined in a population. However, we find that the factors and factor loadings are well identified by the PCA method regardless of the boundedness of the factors’ variance. Moreover, we obtain the asymptotic distributions of the estimated factors and factor loadings by the PCA method. We also provide a structural interpretation of the factor model and model selection criteria for the number of factors as well as the number of structural factors under our structural interpretation of the model. As an empirical application, we apply our methods to the FRED-MD data, and find that some macro factors are highly fat tailed and/or highly persistent.