Authors: Pierluigi Vallarino (Research Fellow at the Econometrics Institute of Erasmus School of Economics), Federico Carlini (Assistant Professor at LUISS Guido Carli) and Mirco Rubin (Associate Professor at EDHEC Nice)
Abstract: We propose a new rank-based test for the number of common primitive shocks q in large panels of observations. After estimating a VAR(1) model on 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 primitive 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.
Abstract: We propose a new rank-based test for the number of common primitive shocks q in large panels of observations. After estimating a VAR(1) model on 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 primitive 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.