HIGH-DIMENSIONAL COVARIANCE MATRICES UNDER DYNAMIC VOLATILITY MODELS: ASYMPTOTICS AND SHRINKAGE ESTIMATION

• 成果类型: Article
• 署名作者: Ding, Yi; Zheng, Xinghua
• 署名单位: University of Macau; Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2381
• 发表日期: 2024
• 页码: 1027-1049
• 关键词: NONLINEAR SHRINKAGE; spectrum

摘要

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 distribution (LSD) of the sample covariance matrix under scalar BEKK models is different from the i.i.d. case. We then propose a time-variation adjusted (TV-adj) sample covariance matrix and prove that its LSD follows the Marcenko-Pastur law. Based on the asymptotics of the TV-adj sample covariance matrix, we develop a consistent population spectrum estimator and an asymptotically optimal nonlinear shrinkage estimator of the unconditional covariance matrix.