New rank-based tests and estimators for Common Primitive Shocks

Federico Carlini, Mirco Rubin and Pierluigi Vallarino
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Federico Carlini: LUISS Business School
Mirco Rubin: EDHEC Business School
Pierluigi Vallarino: Erasmus University Rotterdam and Tinbergen Institute

No 25-016/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

JEL-codes: C12 C23 C38 (search for similar items in EconPapers)
Date: 2025-03-07
New Economics Papers: this item is included in nep-ets
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