A method for extracting the scaling exponents of a self-affine, non-Gaussian process from a finite length timeseries.

Details A method for extracting the scaling exponents of a self-affine, non-Gaussian process from a finite length timeseries. A method for extracting the scaling exponents of a self-affine, non-Gaussian process from a finite length timeseries.

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufmsh13a0407k&link_type=abstract

American Geophysical Union, Fall Meeting 2006, abstract #SH13A-0407

Mathematics

Probability

4425 Critical Phenomena, 4440 Fractals And Multifractals, 4468 Probability Distributions, Heavy And Fat-Tailed (3265), 4490 Turbulence (3379, 4568, 7863)

Scientific paper

We address the generic problem of extracting the scaling exponents of a stationary, self-affine process realised by a timeseries of finite length, where information about the process is not known a priori. Estimating the scaling exponents relies upon estimating the moments, or more typically structure functions, of the probability density of the differenced timeseries. If the probability density is heavy tailed, outliers strongly influence the scaling behaviour of the moments. From an operational point of view, we wish to recover the scaling exponents of the underlying process by excluding a minimal population of these outliers. We test these ideas on a synthetically generated symmetric alpha-stable Levy process and show that the Levy exponent is recovered in up to the 6th order moment after only ~0.1-0.5% of the data are excluded. The scaling properties of the excluded outliers can then be tested to provide additional information about the system.

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