Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/315152 
Year of Publication: 
2025
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2025-016/III
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
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. The new 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. We illustrate our testing and estimation procedures with applications to panels of macroeconomic variables and individual stocks' volatilities.
Subjects: 
Common primitive shocks
Dynamic factor models
Rank tests
Distribution of eigenvalues
Principal component analysis
JEL: 
C12
C23
C38
Document Type: 
Working Paper

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