NONPARAMETRIC ESTIMATION OF LARGE SPOT VOLATILITY MATRICES FOR HIGH-FREQUENCY FINANCIAL DATA

• DOI: 10.1017/s0266466624000264
• Publication Date: 2025-04-07T08:26:00Z
• Authors: Ruijun Bu; Degui Li; Oliver Linton; Hanchao Wang

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