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Asymptotics of the principal components estimator of large factor models with weak factors and i.i.d. Gaussian noise

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  • Onatski, A.

Abstract

We consider large factor models where factors' explanatory power does not strongly dominate the explanatory power of the idiosyncratic terms asymptotically. We find the first and second order asymptotics of the principal components estimator of such a weak factors as the dimensionality of the data and the number of observations tend to infinity proportionally. The principal components estimator is inconsistent but asymptotically normal.

Suggested Citation

  • Onatski, A., 2018. "Asymptotics of the principal components estimator of large factor models with weak factors and i.i.d. Gaussian noise," Cambridge Working Papers in Economics 1808, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:1808
    Note: ao319
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    References listed on IDEAS

    as
    1. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    2. Bai, Z. D. & Silverstein, Jack W. & Yin, Y. Q., 1988. "A note on the largest eigenvalue of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 166-168, August.
    3. Mario Forni & Lucrezia Reichlin, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 453-473.
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    Cited by:

    1. Andreou, Elena & Ghysels, Eric, 2021. "Predicting the VIX and the volatility risk premium: The role of short-run funding spreads Volatility Factors," Journal of Econometrics, Elsevier, vol. 220(2), pages 366-398.
    2. Alexei Onatski & Chen Wang, 2021. "Spurious Factor Analysis," Econometrica, Econometric Society, vol. 89(2), pages 591-614, March.
    3. Jungjun Choi & Ming Yuan, 2024. "High Dimensional Factor Analysis with Weak Factors," Papers 2402.05789, arXiv.org.

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    More about this item

    Keywords

    Large factor models; principal components; phase transition; weak factors; inconsistency; asymptotic distribution; Marčenko-Pastur law;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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