The Convergence Rates of Large Volatility Matrix Estimator Based on Noise, Jumps, and Asynchronization

At the turn of the 21st century, the wide availability of high-frequency data aroused an increasing demand for better modeling and statistical inference. A challenging problem in statistics and econometrics is the estimation problem of the integrated volatility matrix based on high-frequency data. The existing estimators work well for diffusion processes with micro-structural noise and may get worse when jumps are considered. This paper proposes a novel estimation in the presence of jumps, micro-structural noise, and asynchronization. First, we adopt sub-sampling to synchronize the high-frequency data. Then, we use a two-time scale to realize co-volatility to handle noise. Finally, we employ the threshold parameters to remove the effect of jumps and sparsity in two steps. Both the minimax bound and the convergence rate are discussed in the paper. The estimation procedures of the heavy-tailed data will be solved in the future.