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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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    References listed on IDEAS

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    3. Lorenzo Trapani, 2018. "A Randomized Sequential Procedure to Determine the Number of Factors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1341-1349, July.
    4. E. Andreou & P. Gagliardini & E. Ghysels & M. Rubin, 2019. "Inference in Group Factor Models With an Application to Mixed‐Frequency Data," Econometrica, Econometric Society, vol. 87(4), pages 1267-1305, July.
    5. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1217-1232, December.
    6. Jörg Breitung & Uta Pigorsch, 2013. "A Canonical Correlation Approach for Selecting the Number of Dynamic Factors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(1), pages 23-36, February.
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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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