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Testing super-diagonal structure in high dimensional covariance matrices

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  • He, Jing
  • Chen, Song Xi

Abstract

The covariance matrices are essential quantities in econometric and statistical applications including portfolio allocation, asset pricing and factor analysis. Testing the entire covariance under high dimensionality endures large variability and causes a dilution of the signal-to-noise ratio and hence a reduction in the power. We consider a more powerful test procedure that focuses on testing along the super-diagonals of the high dimensional covariance matrix, which can infer more accurately on the structure of the covariance. We show that the test is powerful in detecting sparse signals and parametric structures in the covariance. The properties of the test are demonstrated by theoretical analyses, simulation and empirical studies.

Suggested Citation

  • He, Jing & Chen, Song Xi, 2016. "Testing super-diagonal structure in high dimensional covariance matrices," Journal of Econometrics, Elsevier, vol. 194(2), pages 283-297.
    • Handle: RePEc:eee:econom:v:194:y:2016:i:2:p:283-297
    DOI: 10.1016/j.jeconom.2016.05.007
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    References listed on IDEAS

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    More about this item

    Keywords

    Bandable covariance; High dimensionality; Sparse covariance matrix; Multiple testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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