Scaling collapse and structure functions: identifying self-affinity in finite length time series
1Space and Astrophysics, University of Warwick, UK
2British Antarctic Survey (NERC), Cambridge, UK
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.
Chapman, S. C., Hnat, B., Rowlands, G., and Watkins, N. W.: Scaling collapse and structure functions: identifying self-affinity in finite length time series, Nonlin. Processes Geophys., 12, 767-774, doi:10.5194/npg-12-767-2005, 2005.