Scaling collapse and structure functions: identifying self-affinity in finite length time series S. C. Chapman1, B. Hnat1, G. Rowlands1, and N. W. Watkins2 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.
Citation: 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.