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New rank-based tests and estimators for Common Primitive Shocks

Author

Listed:
  • Federico Carlini

    (LUISS Business School)

  • Mirco Rubin

    (EDHEC Business School)

  • Pierluigi Vallarino

    (Erasmus University Rotterdam and 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.

Suggested Citation

  • Federico Carlini & Mirco Rubin & Pierluigi Vallarino, 2025. "New rank-based tests and estimators for Common Primitive Shocks," Tinbergen Institute Discussion Papers 25-016/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20250016
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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