高频数据下积分波动率矩阵的伪似然估计、预测及应用  

Quasi Maximum Likelihood Estimation,Prediction of the Integrated Covariance Matrix with High Frequency Data and Their Applications in Financial Market

作　　者：刘成 罗金斗 罗知[1] Liu Cheng;Luo Jindou;Luo Zhi(Economics and Management School,Wuhan University)

机构地区：[1]武汉大学经济与管理学院

出　　处：《数量经济技术经济研究》2022年第3期170-188,F0003,共20页Journal of Quantitative & Technological Economics

基　　金：国家自然科学基金重点项目“技术赋能的商务信息全景化管理与增强型决策的人机协同新范式”(72132008);2020年度教育部人文社会科学研究青年基金项目“基于高频数据的积分波动率矩阵动态建模及其在风险控制中的应用研究”(20YJC790074)的资助。

摘　　要：研究目标:利用高频数据准确估计和预测高维积分波动率矩阵,并将矩阵的预测值应用于资产投资组合的构造中。研究方法:通过保留p×p维已实现波动率矩阵的特征向量,对积分波动率矩阵的特征值进行预测,本文将积分波动率矩阵的估计和预测问题转化为p个一维积分波动率的估计和预测问题。研究发现:对高维已实现波动率矩阵过于发散的特征值进行调整能够提高矩阵估计的准确性;对资产收益率的积分波动率矩阵建立动态模型可以提高矩阵预测的精度。研究创新:将高维矩阵的估计和预测问题转化为矩阵特征向量的估计以及一维特征值的估计和预测问题;基于高频数据并建立资产收益率积分波动率矩阵的动态模型提高了资产投资组合的样本外表现。研究价值:本文提出的积分波动率矩阵估计和预测方法能够保证矩阵估计值和预测值的正定性;本文的预测方法能够提高矩阵的预测精度,能够在复杂的金融市场中构造低风险的资产组合。Research Objectives:This paper focuses on the estimation and prediction of a high dimensional integrated covariance matrix(ICM)based on high frequency data.The proposed matrix predictor is then applied to the portfolio constructions with financial assets.Research Methods:The eigenvectors of the estimator and predictor of the ICM are estimated by the eigenvectors of the realized covariance matrix constructed based on the historical high frequency data,where the eigenvalues of them are estimated by the integrated volatilities of p transformed processes of asset prices,and then predicted by the HARQ model.Research Findings:We can improve the accuracy of estimation of the realized covariance matrix by regularizing its eigenvalues when the matrix dimension is high.Constructing a dynamic model for the ICMs is useful for predicting the ICM in the future.Research Innovations:Based on a reasonable assumption,we transform the estimation and prediction of a high dimensional covariance matrix to p one dimensional estimation and prediction problems such that we can decrease the order of the number of parameters and ensure the matrix estimator and predictor to be positive definite simultaneously.By predicting the future ICM based on a dynamic model for the ICMs and with high frequency data,we provide a novel method to construct portfolios with better out of sample performances.Research Value:The estimation and prediction methods for the ICM based on high frequency can ensure the estimator and predictor to be positive definite.This paper gives a novel method for the prediction of the ICM based on high frequency and high dimensional data,which can be used for constructing portfolios with lower out of sample risks.

关 键 词：高维积分波动率矩阵 高频数据 微观结构噪声 资产投资组合 

分 类 号：F830.59[经济管理—金融学]