Testing High-Dimensional Covariance Matrices Under the Elliptical Distribution and Beyond

31 Pages Posted: 19 Jul 2017 Last revised: 15 Jun 2020

See all articles by Xinxin Yang

Xinxin Yang

Central University of Finance and Economics

Xinghua Zheng

Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management

Jiaqi Chen

Harbin Institute of Technology

Date Written: July 13, 2017

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, self-normalization

JEL Classification: C12, C55

Suggested Citation

Yang, Xinxin and Zheng, Xinghua and Chen, Jiaqi, Testing High-Dimensional Covariance Matrices Under the Elliptical Distribution and Beyond (July 13, 2017). Journal of Econometrics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3001811 or http://dx.doi.org/10.2139/ssrn.3001811

Xinxin Yang

Central University of Finance and Economics ( email )

Beijing
China

Xinghua Zheng (Contact Author)

Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management ( email )

Clear Water Bay
Kowloon
Hong Kong

Jiaqi Chen

Harbin Institute of Technology ( email )

92 West Dazhi Street
Nan Gang District
Harbin, heilongjiang 150001
China

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