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

Abstract

[1] 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 Levy 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-a-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.