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

Xinxin Yang, Xinghua Zheng and Jiaqi Chen

Journal of Econometrics, 2021, vol. 221, issue 2, 409-423

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.

Keywords: Covariance matrix; High-dimension; Elliptical model; Linear spectral statistics; Central limit theorem (search for similar items in EconPapers)
JEL-codes: C12 C55 C58 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:221:y:2021:i:2:p:409-423

DOI: 10.1016/j.jeconom.2020.05.017

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