Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data

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.

Estimation of Common Factors for Microstructure Noise and Efficient Price in a High-frequency Dual Factor Model

We develop the Double Principal Component Analysis (DPCA) based on a dual factor structure for high-frequency intraday returns data contaminated with microstructure noise. The dual factor structure allows a factor structure for the microstructure noise in addition to the factor structure for efficient log-prices. We construct estimators of factors for both efficient log-prices and microstructure noise as well as their common components, and provide uniform consistency of these estimators when the number of assets and the sampling frequency go to infinity.

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