高频金融数据的高维积分波动率矩阵估计

High-dimensional integrated volatility matrix estimation for high-frequency financial data

高维积分波动率矩阵是资源配置和风险管理的重要统计量,对其估计是金融统计和风险度量中的热点和核心问题之一.本文在带有市场信息的微观结构噪声下,考虑了高频金融数据大量资产的积分波动率矩阵估计问题.在多资产价格观察不同步下,当资产数和样本量都趋向于无穷时,本文利用不重叠区间方法和稀疏性特征提出了高维积分波动率矩阵估计,证明了该估计量具有相合性,较在加性噪声下的估计具有更快的收敛速度,其收敛速度可以达到已存在高维积分波动率矩阵估计在无噪声下的最快收敛速度.对所提出的估计与现有的高维积分波动率矩阵估计进行模拟比较,结果表明本文提出的估计方法具有优良的性质.最后将提出的估计应用于上海证券指数数据的实证研究中.

High-dimensional integrated volatility matrix is an important statistic for portfolio allocation and financial risk management. Its estimation is a hot core issue in financial statistics and risk measurement. In this paper, we consider the integrated volatility matrix estimated problem of a large number of assets by using asynchronous high-frequency financial data modeling in microstructure noise with market information. When both the number of the assets and the average sample size of the price data on the assets go to infinity, this paper proposes new consistent estimators by using the non-overlapping intervals previous tick method and sparsity technique. Meanwhile, the new estimators have faster convergence rates, equivalently the best convergence rate without noise, than existed estimators under additive noise. The simulation compare and demonstrate that the proposed estimators perform much better than the existed volatility matrix estimators. Finally, the proposed method is applied to the index data of different Shanghai industries.