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• W2018509194 abstract "The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of non-stationary 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 (MFDFA). 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." @default.
• W2018509194 created "2016-06-24" @default.
• W2018509194 creator A5061944773 @default.
• W2018509194 creator A5075941726 @default.
• W2018509194 date "2010-07-27" @default.
• W2018509194 modified "2023-10-11" @default.
• W2018509194 title "Detrending moving average algorithm for multifractals" @default.
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• W2018509194 doi "https://doi.org/10.1103/physreve.82.011136" @default.
• W2018509194 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/20866594" @default.
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