High-dimensional covariance matrices under dynamic volatility models: Asymptotics and shrinkage estimation
研究了动态波动率模型下高维协方差矩阵的估计，提出了时间调整样本协方差矩阵，并基于其渐近性质开发了总体谱估计器和最优非线性收缩估计器。
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 Marčenko–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.