Nonlinear shrinkage estimation of large integrated covariance matrices
针对日内资产收益模型中大维积分协方差矩阵的估计问题，提出一种非线性收缩估计量，通过压缩极端特征值来修正偏差，并在资产数量与数据点数量同阶时具有渐近有效性，可用于构建最小方差投资组合。
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.