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.
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(MFCCA)proposed by O s′wiecimka preserves the sign of the cross-covariances and settles the trouble above.MFCCA is a natural general extension of MFDFA and DCCA.Here it was demonstrated that MFCCA performs more effectively and powerfully than MFDXA 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.
基金
Supported by the National Natural Science Foundation of China(11471304,11401556)
the Fundamental Research Funds for the Central Universities(WK2040000012)
