中国金属期货与现货市场多元交互关系的多重分形分析

Multifractal analysis of the multivariate cross-correlation between metal futures and spot markets in China

本文主要运用分形分析法研究我国金属期货与现货市场之间多元交互关系的复杂性特征.首先将广泛使用的多重分形去趋势交互相关分析法(MF-DCCA)推广至多元情形,提出了多元多重分形去趋势交互相关分析法(MV-MFDCCA).然后,利用MV-MFDCCA等多重分形分析法,从系统论的视角,实证研究由我国铜、铝、锌三种基本金属的期货与现货日收益率序列所构成的两个系统之间的多元交互相关关系.结果表明,金属期货与现货系统内部及系统之间均存在长程幂律交互相关关系和多重分形特征,并且现货系统及其分量的自相关和交互相关关系的多重分形强度均大于期货系统及其对应分量的多重分形强度.此外,在大波动情形下,期货系统与现货系统之间的交互关系主要受铜的期货与现货之间关系的影响,而在小波动情形下,主要受锌的期货与现货之间关系的影响.

In this paper,fractal analysis methods are used to study the complexity characteristics of multivariate cross-correlations between the metal futures and spot markets in China.Firstly,the widely used multifractal detrended cross-correlation analysis(MF-DCCA)is extended to multivariate case,and the multivariate multifractal detrended cross-correlation analysis(MV-MFDCCA)is proposed.Then,the daily returns series of the futures and spot markets for China’s basic metal copper,aluminum and zinc are regarded as two systems,and the multifractal analysis methods including the MV-MFDCCA are used to empirically investigate the multivariate cross-correlation between the two systems from the perspective of system theory.The results show that there are long-range power law cross-correlations and multifractal characteristics within and between the two systems,and the multifractal strengths of autocorrelations and cross-correlations for the spot system and its components are greater than those of the futures system and its corresponding components.In addition,in the situation of large fluctuations,the cross-correlation between the futures and spot systems is mainly influenced by the relationship between the futures copper and spot copper,while in the small fluctuation situation,mainly influenced by the relationship between the futures zinc and spot zinc.