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Title: Testing high-dimensional covariance matrices under the elliptical distribution and beyond Authors:  Xinxin Yang - ISOM, HKUST (Hong Kong) [presenting]
Xinghua Zheng - HKUST (China)
Jiaqi Chen - Harbin Institute of Technology (China)
Hua Li - Chang Chun University (China)
Abstract: High-dimensional covariance matrices testing is studied under a generalized elliptical model. The model accommodates several stylized facts of real data including heteroskedasticity, heavy-tailedness, asymmetry, etc. We consider the high-dimensional setting where the dimension $p$ and the sample size $n$ grow to infinity proportionally, and establish a central limit theorem (CLT) for the linear spectral statistic (LSS) of the sample covariance matrix based on self-normalized observations. The CLT is different from the existing ones for the LSS of the usual sample covariance matrix. Our tests based on the new CLT neither assume a specific parametric distribution nor involve the kurtosis of data. Simulation studies show that our tests work well even when the fourth moment does not exist. Empirically, we analyze the idiosyncratic returns under the Fama-French three-factor model for SP 500 Financials sector stocks, and our tests reject the hypothesis that the idiosyncratic returns are uncorrelated.