| Residential College | false |
| Status | 已發表Published |
| High dimensional covariance matrices under dynamic volatility models: asymptotics and shrinkage estimation | |
DING YI1 ; ZHENG, Xinghua2
| |
| 2024-08 | |
| Source Publication | The Annals of Statistics
 |
| Volume | 52Pages:1027–1049 |
| Abstract | We study the estimation of high-dimensional covariance matrices and their empirical spectral distributions under dynamic volatility models. Data under such models have nonlinear dependency both cross-sectionally and temporally. We establish the condition under which the limiting spectral dis- tribution (LSD) of the sample covariance matrix under scalar BEKK mod- els is different from the i.i.d. case. We then propose a time-variation ad- justed (TV-adj) sample covariance matrix and prove that its LSD follows the Marcˇenko–Pastur law. Based on the asymptotics of the TV-adj sample co- variance matrix, we develop a consistent population spectrum estimator and an asymptotically optimal nonlinear shrinkage estimator of the unconditional covariance matrix. |
| Keyword | High-dimension Dynamic Volatility Model Sample Covariance Matrix Spectral Distribution Nonlinear Shrinkage |
| DOI | https://doi.org/10.1214/24-AOS2381 |
| Language | 英語English |
| Fulltext Access | |
| Citation statistics | |
| Document Type | Journal article |
| Collection | Faculty of Business Administration DEPARTMENT OF FINANCE AND BUSINESS ECONOMICS |
| Corresponding Author | ZHENG, Xinghua |
| Affiliation | 1.University of Macau 2.HKUST |
| First Author Affilication | University of Macau |
| Recommended Citation GB/T 7714 | DING YI,ZHENG, Xinghua. High dimensional covariance matrices under dynamic volatility models: asymptotics and shrinkage estimation[J]. The Annals of Statistics, 2024, 52, 1027–1049. |
| APA | DING YI., & ZHENG, Xinghua (2024). High dimensional covariance matrices under dynamic volatility models: asymptotics and shrinkage estimation. The Annals of Statistics, 52, 1027–1049. |
| MLA | DING YI,et al."High dimensional covariance matrices under dynamic volatility models: asymptotics and shrinkage estimation".The Annals of Statistics 52(2024):1027–1049. |
| Files in This Item: | Download All | |||||
| File Name/Size | Publications | Version | Access | License | ||
| aos2381.pdf（1220KB） | 期刊论文 | 作者接受稿 | 开放获取 | CC BY-NC-SA | View Download | |
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