Scaling collapse and structure functions: Identifying self-affinity in finite length time series

Details Scaling collapse and structure functions: Identifying self-affinity in finite length time series Scaling collapse and structure functions: Identifying self-affinity in finite length time series

2005-04-04

arxiv.org/abs/physics/0504024v2

Nonlinear Processes in Geophysics, 12, 767-774 (2005)

Physics

Fluid Dynamics

Submitted Nonlinear Processes in Geophysics, 18 pages including 8 figures

Scientific paper

Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of self affine time series in the context of a stochastic process. We highlight two complementary approaches to the differenced variable of the data: i) attempting a scaling collapse of the Probability Density Functions which should then be well described by the solution of the corresponding Fokker-Planck equation and ii) using structure functions to determine the scaling properties of the higher order moments. Using the example of a L\'{e}vy flight, we demonstrate a method for conditioning the time series that recovers the underlying self affine scaling in a finite length time series.

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