We propose a new estimator of high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure from noisy and asynchronous high-frequency data collected for an ultra-large number of assets. The noise processes are allowed to be temporally correlated, heteroskedastic, asymptotically vanishing and dependent on the efficient prices. We define a kernel-weighted pre-averaging method to jointly tackle the microstructure noise and asynchronicity issues, and we obtain uniformly consistent estimates for latent prices. We impose a continuous-time factor model with time-varying factor loadings on the price processes, and estimate the common factors and loadings via a local principal component analysis. Assuming a uniform sparsity condition on the idiosyncratic volatility structure, we combine the POET and kernel-smoothing techniques to estimate the spot volatility matrices for both the latent prices and idiosyncratic errors. Under some mild restrictions, the estimated spot volatility matrices are shown to be uniformly consistent under various matrix norms. We provide Monte-Carlo simulation and empirical studies to examine the numerical performance of the developed estimation methodology.

翻译：本文针对大量资产的噪声异步高频数据，提出一种满足低秩加稀疏结构的高维瞬时波动率矩阵的新估计量。噪声过程允许存在时间相关性、异方差性、渐近衰减性以及与有效价格的依赖性。我们定义了一种核加权预平均方法以联合解决微观结构噪声与异步性问题，并获得潜在价格的一致估计。对价格过程施加含有时变因子载荷的连续时间因子模型，通过局部主成分分析法估计共同因子与载荷。在特质波动结构满足均匀稀疏性假设下，结合POET与核平滑技术估计潜在价格及特质误差的瞬时波动率矩阵。在温和约束条件下，所估计的瞬时波动率矩阵在各种矩阵范数下被证明具有一致收敛性。我们通过蒙特卡洛模拟与实证研究检验了所提估计方法的数值表现。