Qiang Liu, Yiming Liu, Zhi Liu, Wang Zhou
arXiv 4 Nov 2025 · Mathematics — Statistics Theory · publishedJournal of Multivariate Analysis (2026)
arXiv:2511.02660 · PDF · DOI · OpenAlex · Extracted main text
In random matrix theory, the spectral distribution of the covariance matrix has been well studied under the large dimensional asymptotic regime when the dimensionality and the sample size tend to infinity at the same rate. However, most existing theories are built upon the assumption of independent and identically distributed samples, which may be violated in practice. For example, the observational data of continuous-time processes at discrete time points, namely, the high-frequency data. In this paper, we extend the classical spectral analysis for the covariance matrix in large dimensional random matrix to the spot volatility matrix by using the high-frequency data. We establish the first-order limiting spectral distribution and obtain a second-order result, that is, the central limit theorem for linear spectral statistics. Moreover, we apply the results to design some feasible tests for the spot volatility matrix, including the identity and sphericity tests. Simulation studies justify the finite sample performance of the test statistics and verify our established theory.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Zheng, X. and Li, Y (2011) On the estimation of integrated covariance matrices of high dmensional diffusion processes | 1.000 | 11 | 4 | 100% |
| 2 | Yang, Xinxin and Zheng, Xinghua and Chen, Jiaqi (2021) Testing high-dimensional covariance matrices under the elliptical distribution and beyond | 1.000 | 5 | 5 | 100% |
| 3 | Bai, Zhidong and Silverstein, Jack W (2010) Spectral Analysis of Large Dimensional Random Matrices | 0.928 | 4 | 4 | 100% |
| 4 | Silverstein, Jack W (1995) Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices | 0.811 | 4 | 2 | 100% |
| 5 | Bai, Zhidong and Jiang, Dandan and Yao, Jian-Feng and Zheng, Shurong (2009) Corrections to LRT on large-dimensional covariance matrix by RMT | 0.693 | 6 | 1 | 100% |
| 6 | Ledoit, Olivier and Wolf, Michael (2002) Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size | 0.693 | 5 | 1 | 100% |
| 7 | T. W. Anderson (2003) An Introduction to Multivariate Statistical Analysis | 0.644 | 2 | 2 | 100% |
| 8 | Y. Aït-Sahalia and J. Jacod (2014) High-Frequency Financial Econometrics | 0.644 | 2 | 2 | 100% |
| 9 | Aït-Sahalia, Y. and Xiu, D (2017) Using principal component analysis to estimate a high dimensional factor model with high-frequency data | 0.644 | 2 | 2 | 100% |
| 10 | R. Bu and D. Li and O. Linton and H. Wang (2025) Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data | 0.644 | 2 | 2 | 100% |
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