带跳高频数据下高维积分波动率矩阵估计  

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

作　　者：穆燕 周勇[2] Yan Mu;Yong Zhou

机构地区：[1]南京财经大学经济学院统计系,南京210023 [2]华东师范大学统计交叉科学研究院和统计学院,统计与数据科学前沿理论及应用教育部重点实验室,上海200062

出　　处：《中国科学：数学》2020年第10期1455-1486,共32页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:71931004,91546202和71901118)资助项目。

摘　　要：资产的联合波动率矩阵是资源配置和风险管理的重要统计量,对其准确估计是金融统计和风险度量中的热点问题之一.本文在带有市场信息的微观结构噪声下,研究带跳对数价格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,利用不重叠区间方法和稀疏性特征提出高维积分波动率矩阵的4种估计方法,其收敛速度可以达到已存在高维积分波动率矩阵估计的最优收敛速度.同时,所提出的调整估计量具有相合性和半正定性.模拟研究中比较了这些估计量的优缺点,并将其应用于上海证券指数数据的实证研究中.The joint volatility matrix of assets is an important statistic for resource allocation and risk management.Accurate estimation of the joint volatility matrix is one of the hot issues in financial statistics and risk measurement.In this paper,we study the integral volatility matrix estimation of logarithmic price data with jumps under microstructure noise including market information.When the prices are not synchronized,and the number of assets and sample size tend to infinity,four estimation methods of high-dimensional integral volatility matrices are proposed by using the non-overlapping interval method and sparse characteristics.The convergence rate can reach the optimal convergence rate of the existing high-dimensional integral volatility matrix estimation.At the same time,the proposed adjusted estimators are consistent and semi-positive definite.The advantages and disadvantages of these estimators are compared in the simulation study.Finally the proposed methods are applied to the empirical study of Shanghai Securities Index data.

关 键 词：高频数据 跳 市场微观结构 高维波动率矩阵 半正定性 

分 类 号：F832.51[经济管理—金融学] F224