Design-free estimation of integrated covariance matrices for high-frequency data

Abstract

The presence of microstructure noise presents a major challenge for estimating the integrated covariance matrices based on high-frequency data. In this paper, we introduce a new method for estimating the integrated covariance matrices that exploits a nonlinear-shrinkage estimation strategy in the high-dimensional setting and a de-noising method in the univariate case. Our estimator is design-free: no structure assumptions are made on the volatility matrix process. We also show that our proposed estimator not only is asymptotically positive definite, but also enjoys a certain desirable estimation efficiency. At last, simulations and financial applications show that the our estimator performs well in comparison with other existing methods.