Multifractality attributed to dual central limitlike convergence effects
Abstract
Multifractals can be defined as fractal systems that express a range of fractal dimensions. The origins of multifractality in time series data have conventionally been attributed to fattailed probability distributions, and to longrange correlations. Multifractal sequences can be generated from the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles of random matrix theory. These deviations can be resolved into component monofractal sequences governed by the Tweedie compound Poisson distribution, a statistical model that expresses a variance to mean power law related to longrange correlations. Fully multifractal descriptions of these deviations can be constructed, provided that the parameter of the compound Poisson model related to fractal dimension varies in accordance with an asymmetric Laplace distribution. Both the Tweedie compound Poisson distribution and the asymmetric Laplace distribution serve as foci of convergence in limit theorems on independent and identically distributed random variables. The hypothesis that multifractal sequences can be attributed to mathematical convergence effects that have as their focus these two statistical models is proposed.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 May 2014
 DOI:
 10.1016/j.physa.2014.01.022
 Bibcode:
 2014PhyA..401...22K