Apparent/spurious multifractality of absolute increments sampled from truncated fractional Gaussian/Lévy noise

Details Apparent/spurious multifractality of absolute increments sampled from truncated fractional Gaussian/Lévy noise Apparent/spurious multifractality of absolute increments sampled from truncated fractional Gaussian/Lévy noise

May 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010georl..3709403n&link_type=abstract

Geophysical Research Letters, Volume 37, Issue 9, CiteID L09403

Mathematics

Logic

1

Nonlinear Geophysics: Fractals And Multifractals, Nonlinear Geophysics: Scaling: Spatial And Temporal (1872, 1988, 3265, 3270, 4277, 7857), Nonlinear Geophysics: Probability Distributions, Heavy And Fat-Tailed (3265), Hydrology: Hydrologic Scaling, Hydrology: Time Series Analysis (1988, 3270, 4277, 4475)

Scientific paper

Many earth and environmental variables appear to scale as multifractals with spatial or temporal increments having exceedance probability tails decaying as powers of -α where 1 < α ≤ 2. The literature considers multifractal scaling to be associated with multiplicative random fields or processes. Elsewhere the author has demonstrated theoretically that square increments, sampled across a finite domain from one or several realizations of additive fractional Gaussian noise (fGn), behave as if the field was multifractal when in fact it is monofractal self-affine; square increments sampled from additive fractional Lévy noise (fLn) with 1 < α < 2 exhibit spurious multifractality. This brief letter demonstrates the same numerically for random absolute increments. The results have broad implications vis-à-vis the scaling of variables considered in the literature to be multifractal, raising the possibility that some if not all may in fact represent truncated monofractal phenomena.

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