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Multifractality attributed to dual central limit-like convergence effects

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  • Kendal, Wayne S.

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 fat-tailed probability distributions, and to long-range 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 long-range 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.

Suggested Citation

  • Kendal, Wayne S., 2014. "Multifractality attributed to dual central limit-like convergence effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 22-33.
    • Handle: RePEc:eee:phsmap:v:401:y:2014:i:c:p:22-33
    DOI: 10.1016/j.physa.2014.01.022
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    Cited by:

    1. Wang, Yanjun & Zhang, Qiqian & Zhu, Chenping & Hu, Minghua & Duong, Vu, 2016. "Human activity under high pressure: A case study on fluctuation scaling of air traffic controller’s communication behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 151-157.
    2. Johann Cuenin & Bent Jørgensen & Célestin C. Kokonendji, 2016. "Simulations of full multivariate Tweedie with flexible dependence structure," Computational Statistics, Springer, vol. 31(4), pages 1477-1492, December.
    3. Cao, Guangxi & Xu, Wei, 2016. "Nonlinear structure analysis of carbon and energy markets with MFDCCA based on maximum overlap wavelet transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 505-523.

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