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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.
The problem of multifractal expansion based on descending cross-over analysis (DCCA) is that it is possible that any moment of the negative cross-covariance can lead to the occurrence of complex values. Usually the modal processing method MFDXA will be used in the absence of fractal features Detection of significant multifractal signal.Os’wiecimka multi-fractal descending trend correlation analysis (MFCCA) retains each sub-interval down covariance symbol this important information to solve the above trouble points, and can accurately identify Multi-fractal interaction signal is a natural extension of descending cross correlation analysis method.From the general form of two-component ARFIMA model, it is proved that MFCCA algorithm is more effective than MFDXA algorithm.MFCCA can correctly identify fractal features, at the same time Which is sensitive to the weight parameter W. In addition, applying the MFCCA algorithm to the Chinese stock market confirms that there is only a fractal characteristic only with large fluctuations in the CSI 300 index quantity and price.