Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm

Abstract

AbstractWe investigate numerically apparent multi‐fractal behavior of samples from synthetically generated processes subordinated to truncated fractional Brownian motion (tfBm) on finite domains. We are motivated by the recognition that many earth and environmental (including hydrological) variables appear to be self‐affine (monofractal) or multifractal with Gaussian or heavy‐tailed distributions. The literature considers self‐affine and multifractal types of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. It has been demonstrated theoretically by one of us that square or absolute increments of samples from Gaussian/Lévy processes subordinated to tfBm exhibit apparent/spurious multifractality at intermediate ranges of separation lags, with breakdown in power‐law scaling at small and large lags as is commonly exhibited by real data. A preliminary numerical demonstration of apparent multifractality by the same author was limited to Gaussian fields having nearest neighbor autocorrelations and led to rather noisy results. Here, we adopt a new generation scheme that allows us to investigate apparent multifractal behaviors of samples taken from a broad range of processes including Gaussian with and without symmetric Lévy and log‐normal (as well as potentially other) subordinators. Our results shed new light on the nature of apparent multifractality, which has wide implications vis‐a‐vis the scaling of many hydrological as well as other earth and environmental variables. Copyright © 2011 John Wiley & Sons, Ltd.