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Testing high-dimensional covariance matrices under the elliptical distribution and beyond

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  • Yang, Xinxin
  • Zheng, Xinghua
  • Chen, Jiaqi

Abstract

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem for linear spectral statistics of the sample covariance matrix based on self-normalized observations. For testing sphericity, our tests neither assume specific parametric distributions nor involve the kurtosis of data. More generally, we can test against any non-negative definite matrix that can even be not invertible. As an interesting application, we illustrate in empirical studies that our tests can be used to test uncorrelatedness among idiosyncratic returns.

Suggested Citation

  • Yang, Xinxin & Zheng, Xinghua & Chen, Jiaqi, 2021. "Testing high-dimensional covariance matrices under the elliptical distribution and beyond," Journal of Econometrics, Elsevier, vol. 221(2), pages 409-423.
    • Handle: RePEc:eee:econom:v:221:y:2021:i:2:p:409-423
    DOI: 10.1016/j.jeconom.2020.05.017
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    2. Dörnemann, Nina, 2023. "Likelihood ratio tests under model misspecification in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

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    More about this item

    Keywords

    Covariance matrix; High-dimension; Elliptical model; Linear spectral statistics; Central limit theorem;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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