文献类型：期刊文献

英文题名：Detrending moving average algorithm for multifractals

作者：Gu, Gao-Feng[1,2];Zhou, Wei-Xing[1,2,3,4,5]

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;[4]E China Univ Sci & Technol, Engn Res Ctr Proc Syst Engn, Minist Educ, Shanghai 200237, Peoples R China;[5]Chinese Acad Sci, Res Ctr Fictitious Econ & Data Sci, Beijing 100080, Peoples R China

年份：2010

卷号：82

期号：1

外文期刊名：PHYSICAL REVIEW E

收录：;EI(收录号：20103113119392);WOS:【SCI-EXPANDED(收录号:WOS:000280369800001)】；

基金：We acknowledge financial support from the Fundamental Research Funds for the Central Universities and the Program for New Century Excellent Talents in University (Grant No. NCET-07-0288).

语种：英文

外文关键词：Fractals

摘要：The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter theta determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward (theta=0), centered (theta=0.5), and forward (theta=1) detrending windows. We find that the estimated multifractal scaling exponent tau(q) and the singularity spectrum f(alpha) are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.