中文摘要：

基于降趋交叉分析法(DCCA)的多重分形情形拓展存在麻烦点,即负的交叉协方差的任意矩可能会导致复值的出现.通常采取模的处理方法 MFDXA会在实际没有分形特征情形下检测出明显的多重分形信号.Os′wiecimka提出的多重分形降趋交互相关性分析法(MFCCA)保留了每个子区间降趋协方差符号这一重要信息,解决了上述麻烦点,同时能够准确识别多重分形交互关系信号,是降趋交互相关性分析法的自然拓展.这里从一般形式两成分ARFIMA模型的角度出发,证明了MFCCA算法相比MFDXA算法更加有效.MFCCA能够正确地识别分形特征,同时对权重参数W表现出一定的敏感性.此外,将MFCCA算法应用于中国股票市场上,证实了CSI 300指数量价间只有大的波动才具有分形特征.

英文摘要：

Multifractal extension of detrended cross‐correlation analysis (DCCA ) usually involves the trouble that the computation of arbitrary powers of the negative cross‐covariances leads to complex values . However , a commonly adopted modulus processing method MFDXA often indicates significant multifractal cross‐correlation signal when actually no fractality exists . Mulitfractal cross‐correlation analysis (M FCCA) proposed by O s′ wiecimka preserves the sign of the cross‐covariances and settles the trouble above .M FCCA is a natural general extension of MFDFA and DCCA . Here it was demonstrated that M FCCA performs more effectively and powerfully than M FDXA from the view of the general two‐component ARFIMA processes model . MFCCA can correctly identify the signal of multifractality behavior and show sensitivity to the varying of the weight parameter W .