  Local scaling and singularity properties of solar wind and geomagnetic time
series were analysed using H\"{o}lder exponents $\alpha$. It was shown that in
analysed cases due to multifractality of fluctuations $\alpha$ changes from
point to point. We argued there exists a peculiar interplay between regularity
/ irregularity and amplitude characteristics of fluctuations which could be
exploited for improvement of predictions of geomagnetic activity. To this end
layered backpropagation artificial neural network model with feedback
connection was used for the study of the solar wind - magnetosphere coupling
and prediction of geomagnetic $D_{st}$ index. The solar wind input was taken
from principal component analysis of interplanetary magnetic field, proton
density and bulk velocity. Superior network performance was achieved in cases
when the information on local H\"{o}lder exponents was added to the input
layer.
