Title: Nonparametric estimation of large spot volatility matrices for high frequency data
Authors: Ruijun Bu - University of Liverpool (United Kingdom) [presenting]
Degui Li - University of York (United Kingdom)
Oliver Linton - University of Cambridge (United Kingdom)
Hanchao Wang - Shandong University (China)
Abstract: The focus is on 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 for low-frequency data. 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 in the high-dimensional setting which first pre-whitens data via a kernel filter and then uses the estimation tool developed in the noise-free scenario. Furthermore, we apply the developed technique to estimate the time-varying volatility matrix of the high-dimensional noise vector, and establish the relevant uniform consistency result. Numerical studies are provided to examine the performance of the proposed estimation methods in finite samples.