  In this paper, we consider estimating spot/instantaneous volatility matrices
of high-frequency data collected for a large number of assets. We first combine
classic nonparametric kernel-based smoothing with a generalised shrinkage
technique in the matrix estimation for noise-free data under a uniform sparsity
assumption, a natural extension of the approximate sparsity commonly used in
the literature. The uniform consistency property is derived for the proposed
spot volatility matrix estimator with convergence rates comparable to the
optimal minimax one. For the high-frequency data contaminated by microstructure
noise, we introduce a localised pre-averaging estimation method that reduces
the effective magnitude of the noise. We then use the estimation tool developed
in the noise-free scenario, and derive the uniform convergence rates for the
developed spot volatility matrix estimator. We further combine the kernel
smoothing with the shrinkage technique to estimate the time-varying volatility
matrix of the high-dimensional noise vector. In addition, we consider large
spot volatility matrix estimation in time-varying factor models with observable
risk factors and derive the uniform convergence property. We provide numerical
studies including simulation and empirical application to examine the
performance of the proposed estimation methods in finite samples.
