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

doi:10.3969/j.issn.0253-2778.2015.08.010

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (8): 683-691.DOI: 10.3969/j.issn.0253-2778.2015.08.010

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

笪婷婷

1.中国科学技术大学管理学院统计与金融系，安徽合肥 230026；2.中国科学技术大学材料科学与工程系，安徽合肥 230026

收稿日期:2014-10-10 修回日期:2015-05-11 出版日期:2015-08-31 发布日期:2015-08-31
作者简介:DA Tingting (corresponding author), female, born in 1991, master. Research field: statistical finance.

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

DA Tingting

1.Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China; 2.Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Received:2014-10-10 Revised:2015-05-11 Online:2015-08-31 Published:2015-08-31
Contact: DA Tingting

摘要/Abstract

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.

Key words: multifractality, cross correlation analysis, detrended analysis, the general two-component ARFIMA processes, price-volume relationship, CSI 300 index

笪婷婷，张曙光，笪诚. 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[J]. 中国科学技术大学学报, 2015, 45(8): 683-691.

DA Tingting, ZHANG Shuguang, DA Cheng. The MFCCA algorithm and its application in financial market: A new view of multifractal extension of DCCA[J]. Journal of University of Science and Technology of China, 2015, 45(8): 683-691.

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

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