Scaling collapse and structure functions: identifying self-affinity in finite length time series
Chapman, Sandra C., Hnat, B., Rowlands, G. (George) and Watkins, Nicholas W.. (2005) Scaling collapse and structure functions: identifying self-affinity in finite length time series. Nonlinear Processes in Geophysics, Vol.12 . pp. 767-774. ISSN 1023-5809
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Official URL: http://www.nonlin-processes-geophys.net/12/767/200...
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:||Journal Article|
|Subjects:||Q Science > QC Physics|
|Divisions:||Faculty of Science > Physics|
|Library of Congress Subject Headings (LCSH):||Geophysics, Time-series analysis, Turbulence, Statistical physics|
|Journal or Publication Title:||Nonlinear Processes in Geophysics|
|Official Date:||3 August 2005|
|Page Range:||pp. 767-774|
|Access rights to Published version:||Open Access|
|Funder:||Science and Technology Facilities Council (Great Britain) (STFC)|
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