多维高频数据的“已实现”波动建模研究

Research on the modelling of realized volatility based on multivariate high-frequency data

金融市场高频数据的分析与建模是金融计量学一个全新的研究领域.把基于一维高频数据的“已实现”波动率扩展到多维高频数据情形,给出“已实现”协方差阵,并给出了协方差阵的极限性质,用以刻画多维金融变量的波动率和相关性.研究了基于上证综指和深圳成份指数高频数据的“已实现”协方差阵的特性,最后针对它的长记忆性建立了FIVAR模型,该模型刻画了上证综指和深圳成份指数各自的波动性和之间的相关性.研究发现,“已实现”波动和“已实现”协方差取对数后具有良好的正态分布特性,相同的长记忆性.针对“已实现”协方差阵建立的FIVAR模型为进一步研究波动的协同持续性提供了基础.

High-frequency financial data analysis and modeling are a new research field in financial econometrics. The paper extends realized volatility based on high-frequency data to realized covariance m trix based on multivariate high-frequency data, to describe volatility and correlation of multivariate. Then the paper studies the characteristics of the realized covariance matrix of Shanghai Composite Index and Shenzhen Component Index, and constructs FIVAR model to its＇ long memory characteristic, to describe their volatility and correlation. The research shows that the realized volatility and the realized covariance after taking logarithm have good normal distribution characteristics and the same long memory characteristics. The FIVAR model based on realized covariance matrix is good basis of studying co-persistence.