Nonlinear shrinkage estimation of large integrated covariance matrices

• 成果类型: Article
• 署名作者: Lam, Clifford; Feng, Phoenix; Hu, Charlie
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx021
• 发表日期: 2017
• 页码: 481488
• 关键词: convergence; volatility; selection; models; Lasso; rates

摘要

Integrated covariance matrices arise in intraday models of asset returns, which allow volatility to change over the trading day. When the number of assets is large, the natural estimator of such a matrix suffers from bias due to extreme eigenvalues. We introduce a novel nonlinear shrinkage estimator for the integrated covariance matrix which shrinks the extreme eigenvalues of a realized covariance matrix back to an acceptable level, and enjoys a certain asymptotic efficiency when the number of assets is of the same order as the number of data points. Novel maximum exposure and actual risk bounds are derived when our estimator is used in constructing the minimum variance portfolio. In simulations and a real-data analysis, our estimator performs favourably in comparison with other methods.