Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes

@article{Heneghan2000EstablishingTR,
  title={Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes},
  author={Heneghan and McDarby},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={2000},
  volume={62 5 Pt A},
  pages={
          6103-10
        }
}
  • Heneghan, McDarby
  • Published 1 November 2000
  • Mathematics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
Stochastic fractal signals can be characterized by the Hurst coefficient H, which is related to the exponents of various power-law statistics characteristic of these processes. Two techniques widely used to estimate H are spectral analysis and detrended fluctuation analysis (DFA). This paper examines the analytical link between these two measures and shows that they are related through an integral transform. Numerical simulations confirm this relationship for ideal synthesized fractal signals… 
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Two extended relationships of the MF-DFA are reexamine and it is demonstrated that the invalidity of the relationship h(q)≡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 is demonstrated.
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