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MFCCA算法及其在金融市场中的应用:DCCA多重分形拓展的新视角

The MFCCA algorithm and its application in financial market: A new view of multifractal extension of DCCA

  • 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.

     

    Abstract: 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 Os′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.

     

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