论文标题
动态波动率模型下的高维协方差矩阵：渐近和收缩估计
High-dimensional covariance matrices under dynamic volatility models: asymptotics and shrinkage estimation
论文作者
论文摘要
我们研究了动态波动率模型下的高维协方差矩阵和特征值的估计。在横截面和时间上，此类模型Shave非线性依赖性下的数据。我们首先对标量BEKK模型下样品协方差质体的经验光谱分布（ESD）进行了研究，并建立了theLimiting Spectral分布（LSD）与I.I.D.或不同的条件。案件。然后，我们提出了一个时间变化调整后的（TV-ADJ）样本共同变异矩阵，并证明其LSD遵循与I.I.D.相同的Marcenko-Pasturlaw。案件。基于TV-ADJ样品共振矩阵的渐近学，我们开发了一致的种群频谱估计器和无条件无条件矩阵的渐近最佳非线性收缩估计器
We study the estimation of the high-dimensional covariance matrix andits eigenvalues under dynamic volatility models. Data under such modelshave nonlinear dependency both cross-sectionally and temporally. We firstinvestigate the empirical spectral distribution (ESD) of the sample covariancematrix under scalar BEKK models and establish conditions under which thelimiting spectral distribution (LSD) is either the same as or different fromthe i.i.d. case. We then propose a time-variation adjusted (TV-adj) sample co-variance matrix and prove that its LSD follows the same Marcenko-Pasturlaw as the i.i.d. case. 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 unconditionalcovariance matrix
