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

Chapman, S.C.; Hnat, B.; Rowlands, G.; Watkins, N.W.. 2005 Scaling collapse and structure functions: identifying self-affinity in finite length time series. Nonlinear Processes in Geophysics, 12 (6). 767-774. https://doi.org/10.5194/npg-12-767-2005

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Abstract/Summary

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. We consider a method of conditioning that recovers the underlying self affine scaling in a finite length time series, and illustrate it using a Lévy flight.

Item Type:	Publication - Article
Digital Object Identifier (DOI):	https://doi.org/10.5194/npg-12-767-2005
Programmes:	BAS Programmes > Antarctic Science in the Global Context (2000-2005) > Magnetic Reconnection, Substorms and their Consequences
ISSN:	1023-5809
Additional Keywords:	Turbulence
NORA Subject Terms:	Physics
Date made live:	20 Dec 2007 12:10 +0 (UTC)
URI:	https://nora.nerc.ac.uk/id/eprint/1696

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