Relationships of exponents in two-dimensional multifractal detrended fluctuation analysis
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AbstractMultifractal detrended fluctuation analysis (MF-DFA) is a generalization of the conventional multifractal analysis. It is extended from the detrended fluctuation analysis (DFA) which is developed for the purpose of detecting long-range correlation and fractal property in stationary and nonstationary time series. The MF-DFA and some corresponding relationships of the exponents have been subsequently extended to the two-dimensional space. We reexamine two extended relationships in this study and demonstrate that: (i) The invalidity of the relationship h(q) equivalent to H for two-dimensional fractional Brownian motion, and h(q = 2) = H between the Hurst exponent H and the generalized Hurst exponent h(q) in the two-dimensional case. Two more logical relationships are proposed instead as h(q = 2) = H for the stationary surface and h(q = 2) = H + 2 for the nonstationary signal. (ii) The invalidity of the expression tau(q) = qh(q) - D-f stipulating the relationship between the standard partition-function-based multifractal exponent tau(q) and the generalized Hurst exponent h(q) in the two-dimensional case. Reasons for its invalidity are given from two perspectives. DOI: 10.1103/PhysRevE.87.012921
All Author(s) ListZhou Y, Leung Y, Yu ZG
Journal namePhysical Review E
Volume Number87
Issue Number1
PublisherAmerican Physical Society
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesPhysics; Physics, Fluids & Plasmas; PHYSICS, FLUIDS & PLASMAS; Physics, Mathematical; PHYSICS, MATHEMATICAL

Last updated on 2021-18-09 at 00:20