High-dimensional covariance matrices under dynamic volatility models: asymptotics and shrinkage estimation
动态波动率模型下的高维协方差矩阵:渐近理论与收缩估计
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…