Apparent multifractality and scale-dependent distribution of data sampled from self-affine processes

作者：Neuman Shlomo P^*

来源：Hydrological Processes, 2011, 25(11): 1837-1840.

DOI：10.1002/hyp.7967

• self-affinity
• multifractality
• heavy-tailed distribution
• fractional levy motion
• fractional Brownian motion

It has been previously demonstrated theoretically and numerically by the author that square or absolute increments of data sampled from fractional Brownian/Levy motion (fBm/fLm), or of incremental data sampled from fractional Gaussian/Levy 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.

• 出版日期2011-5-30