4 research outputs found
A continuous time random walk model for financial distributions
We apply the formalism of the continuous time random walk to the study of
financial data. The entire distribution of prices can be obtained once two
auxiliary densities are known. These are the probability densities for the
pausing time between successive jumps and the corresponding probability density
for the magnitude of a jump. We have applied the formalism to data on the US
dollar/Deutsche Mark future exchange, finding good agreement between theory and
the observed data.Comment: 14 pages, 5 figures, revtex4, submitted for publicatio
Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent than Others?
Multiple recent investigations of solar magnetic field measurements have
raised claims that the scale-free (fractal) or multiscale (multifractal)
parameters inferred from the studied magnetograms may help assess the eruptive
potential of solar active regions, or may even help predict major flaring
activity stemming from these regions. We investigate these claims here, by
testing three widely used scale-free and multiscale parameters, namely, the
fractal dimension, the multifractal structure function and its inertial-range
exponent, and the turbulent power spectrum and its power-law index, on a
comprehensive data set of 370 timeseries of active-region magnetograms (17,733
magnetograms in total) observed by SOHO's Michelson Doppler Imager (MDI) over
the entire Solar Cycle 23. We find that both flaring and non-flaring active
regions exhibit significant fractality, multifractality, and non-Kolmogorov
turbulence but none of the three tested parameters manages to distinguish
active regions with major flares from flare-quiet ones. We also find that the
multiscale parameters, but not the scale-free fractal dimension, depend
sensitively on the spatial resolution and perhaps the observational
characteristics of the studied magnetograms. Extending previous works, we
attribute the flare-forecasting inability of fractal and multifractal
parameters to i) a widespread multiscale complexity caused by a possible
underlying self-organization in turbulent solar magnetic structures, flaring
and non-flaring alike, and ii) a lack of correlation between the fractal
properties of the photosphere and overlying layers, where solar eruptions
occur. However useful for understanding solar magnetism, therefore, scale-free
and multiscale measures may not be optimal tools for active-region
characterization in terms of eruptive ability or, ultimately,for major
solar-flare prediction.Comment: 25 pages, 7 figures, 2 tables, Solar Phys., in pres