文献类型：期刊文献

英文题名：Multifractal detrending moving-average cross-correlation analysis

作者：Jiang, Zhi-Qiang[1,2];Zhou, Wei-Xing[1,2,3]

机构：[1]E China Univ Sci & Technol, Sch Business, Shanghai 200237, Peoples R China;[2]E China Univ Sci & Technol, Res Ctr Econophys, Shanghai 200237, Peoples R China;[3]E China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China

年份：2011

卷号：84

期号：1

外文期刊名：PHYSICAL REVIEW E

收录：;EI(收录号：20113214215975);WOS:【SCI-EXPANDED(收录号:WOS:000293449800001)】；

基金：We are grateful to Jean-Francois Coeurjolly for providing the R code to generate bivariate fractional Brownian motions and to Anna Carbone, Gao-Feng Gu, Boris Podobnik, and Qun-Zhi Zhang for invaluable discussions. This work was partially supported by the National Natural Science Foundation of China under Grant No. 11075054 and the Fundamental Research Funds for the Central Universities.

语种：英文

外文关键词：Numerical methods - Brownian movement - Correlation methods - Fractals

摘要：There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending moving-average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving-average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents h(xy) extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated moving-average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order q < 0 and underperforms when q > 0. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of h(xy) (q) since its h(xy) (2) is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.