Relationships of exponents in multifractal detrended fluctuation analysis and conventional multifractal analysis  

作　　者：周煜 梁怡 喻祖国 

机构地区：[1]Department of Geography and Resource Management,The Chinese University of Hong Kong [2]Center for Environmental Policy and Resource Management,The Chinese University of Hong Kong [3]Institute of Space and Earth Information Science,The Chinese University of Hong Kong [4]Discipline of Mathematical Sciences,Faculty of Science and Technology,Queensland University of Technology [5]School of Mathematics and Computational Science,Xiangtan University

出　　处：《Chinese Physics B》2011年第9期98-106,共9页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No.11071282);the Chinese Program for New Century Excellent Talents in University (Grant No.NCET-08-06867)

摘　　要：Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r（q） = qh（q） - 1 stipulating the relationship between the multifractal exponent T（q） and the generalized Hurst exponent h（q）. As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-（q） = qh（q） - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f（a）, are also derived according to this new relationship.Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r（q） = qh（q） - 1 stipulating the relationship between the multifractal exponent T（q） and the generalized Hurst exponent h（q）. As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-（q） = qh（q） - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f（a）, are also derived according to this new relationship.

关 键 词：fractals Hurst exponent multifractal detrended fluctuation analysis time series analysis 

分 类 号：O415.5[理学—理论物理]