  We investigate the general problem of how to model the kinematics of stock
prices without considering the dynamical causes of motion. We propose a
stochastic process with long-range correlated absolute returns. We find that
the model is able to reproduce the experimentally observed clustering, power
law memory, fat tails and multifractality of real financial time series. We
find that the distribution of stock returns is approximated by a Gaussian with
log-normally distributed local variance and shows excellent agreement with the
behavior of the NYSE index for a range of time scales.
