dorsal/arxiv
View SchemaScaling collapse and structure functions: Identifying self-affinity in finite length time series
| Authors | S. C. Chapman, B. Hnat, G. Rowlands, N. W. Watkins |
|---|---|
| Categories | |
| ArXiv ID | physics/0504024 |
| URL | https://arxiv.org/abs/physics/0504024 |
| DOI | 10.5194/npg-12-767-2005 |
| Journal | Nonlinear Processes in Geophysics, 12, 767-774 (2005) |
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. 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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"abstract": "Empirical determination of the scaling properties and exponents of time\nseries presents a formidable challenge in testing, and developing, a\ntheoretical understanding of turbulence and other out-of-equilibrium phenomena.\nWe discuss the special case of self affine time series in the context of a\nstochastic process. We highlight two complementary approaches to the\ndifferenced variable of the data: i) attempting a scaling collapse of the\nProbability Density Functions which should then be well described by the\nsolution of the corresponding Fokker-Planck equation and ii) using structure\nfunctions to determine the scaling properties of the higher order moments.\nUsing the example of a L\\\u0027{e}vy flight, we demonstrate a method for\nconditioning the time series that recovers the underlying self affine scaling\nin a finite length time series.",
"arxiv_id": "physics/0504024",
"authors": [
"S. C. Chapman",
"B. Hnat",
"G. Rowlands",
"N. W. Watkins"
],
"categories": [
"physics.flu-dyn",
"physics.space-ph"
],
"doi": "10.5194/npg-12-767-2005",
"journal_ref": "Nonlinear Processes in Geophysics, 12, 767-774 (2005)",
"title": "Scaling collapse and structure functions: Identifying self-affinity in finite length time series",
"url": "https://arxiv.org/abs/physics/0504024"
},
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