FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA
针对高频金融数据中资产数量大、存在微观结构噪声和不同步观测的问题，提出一种新的大波动率矩阵估计量，证明其在资产数和样本量都趋于无穷时一致且收敛速率最优，并通过模拟验证有限样本表现。
Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency data. Many existing estimators of a volatility matrix of small dimensions become inconsistent when the size of the matrix is close to or larger than the sample size. This paper introduces a new type of large volatility matrix estimator based on nonsynchronized high-frequency data, allowing for the presence of microstructure noise. When both the number of assets and the sample size go to infinity, we show that our new estimator is consistent and achieves a fast convergence rate, where the rate is optimal with respect to the sample size. A simulation study is conducted to check the finite sample performance of the proposed estimator.