Fast Convergence Rates in Estimating Large Volatility Matrices Using High-Frequency Financial Data

• Activity Number: 309
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Minjing Tao*+ and Yazhen Wang and Xiaohong Chen
• Companies: University of Wisconsin at Madison and University of Wisconsin at Madison and Yale University
• Keywords: large dimensional diffusion ; matrix norm ; micro-structure noise ; multi-scale realized volatility matrix estimator ; sparsity ; threshold

Abstract

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 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 estimators based on non-synchronized high-frequency data, allowing for the presence of micro-structure noise. When both the number of assets and the sample size go to in?nity, we show that our new estimator is consistent and achieves fast convergence rate, where the rate is optimal with respect to the sample size.