多标度条件下资本市场波动的级串方向和结构

Cascade Direction and Structure of Multiscale Volatilities in Capital Markets

对上证综指多标度条件下波动级串方向和结构的实证研究发现，在4days临界标度范围内，大小波动间互为因果；超出临界标度，大小波动间表现出单方向性特征。运用交叉相关系数和功率谱方法从相关性和能量耗散2个角度对多标度波动级串传递方向的分析同样显示，在10^1～10^3min的3个数量级广泛标度范围内，大波动对于小波动具有较强预测能力，波动级串结构表现出大波动影响小波动变化的单方向特征。在此基础上，提出了4类“递进”的资本市场波动级串模型及其运用于风险管理的基本思路。

Cascade direction and structure of multiscale volatilities in SSECI was investigated empirically. The results indicate that there exist the mutual causal relationships between the coarse and fine volatilities within critical timescale of 4 days. When exceeding the criticality, the causal relationships only display the single direction. The additional two measures of crossed correlation coefficient and power spectrum were simultaneously applied to the cascade characteristics of volatility. The further researches suggest that the lagged coarse volatilities can predict well the fine volatilities over three magnitudes of 10^1-10^3min timescale, and that the cascade structure exhibits the single direction from the course to fine volatilities. The framework of four types of cascade model and the basic idea of risk management are also proposed.