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Scaling collapse and structure functions: identifying self-affinity in finite length time series
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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...
Abstract
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 | ||||
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Subjects: | Q Science > QC Physics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||
Library of Congress Subject Headings (LCSH): | Geophysics, Time-series analysis, Turbulence, Statistical physics | ||||
Journal or Publication Title: | Nonlinear Processes in Geophysics | ||||
Publisher: | Copernicus GmbH | ||||
ISSN: | 1023-5809 | ||||
Official Date: | 3 August 2005 | ||||
Dates: |
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Volume: | Vol.12 | ||||
Page Range: | pp. 767-774 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Funder: | Science and Technology Facilities Council (Great Britain) (STFC) |
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