New rank-based tests and estimators for Common Primitive Shocks

Abstract

We propose a new rank-based test for the number of common primitive shocks q in large panel data. After estimating a VAR(1) model on r static factors extracted by principal component analysis, we estimate the number of common primitive shocks by testing the rank of the VAR residuals’ covariance matrix. Our new rank test is based on the asymptotic distribution of the sum of the smallest r − q eigenvalues of the residuals’ covariance matrix. We develop both plug-in and bootstrap versions of this eigenvalue-based test. The eigenvectors associated to the q largest eigenvalues allow us to construct an easy-to-implement estimator of the common shocks and to derive its asymptotic properties. We consider applications of the new tests and estimators on panels of macro-financial variables and individual stocks volatilities. Joint paper with Federico Carlini (LUISS, Rome) and Pierluigi Vallarino (Erasmus University of Rotterdam)