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Apparent multifractality and scale‐dependent distribution of data sampled from self‐affine processes
Author(s) -
Neuman Shlomo P.
Publication year - 2011
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/hyp.7967
Subject(s) - fractional brownian motion , spurious relationship , affine transformation , scale (ratio) , mathematics , distribution (mathematics) , statistical physics , gaussian , brownian motion , scaling , scale invariance , stable distribution , mathematical analysis , statistics , physics , pure mathematics , geometry , quantum mechanics
It has been previously demonstrated theoretically and numerically by the author that square or absolute increments of data sampled from fractional Brownian/Lévy motion (fBm/fLm), or of incremental data sampled from fractional Gaussian/Lévy noise (fGn/fLn), exhibit apparent/spurious multifractality. Here, we generalize these previous development in a way that (a) rigorously subordinates (truncated) fLn to fGn or, in a statistically equivalent manner, (truncated) fLm to fBm; (b) extends the analysis to a wider class of subordinated self‐affine processes; (c) provides a simple way to generate such processes and (d) explains why the distribution of corresponding increments tends to evolve from heavy tailed at small lags (separation distances or scales) to Gaussian at larger lags. Copyright © 2011 John Wiley & Sons, Ltd.