  In setting up a stochastic description of the time evolution of a financial
index, the challenge consists in devising a model compatible with all stylized
facts emerging from the analysis of financial time series and providing a
reliable basis for simulating such series. Based on constraints imposed by
market efficiency and on an inhomogeneous-time generalization of standard
simple scaling, we propose an analytical model which accounts simultaneously
for empirical results like the linear decorrelation of successive returns, the
power law dependence on time of the volatility autocorrelation function, and
the multiscaling associated to this dependence. In addition, our approach gives
a justification and a quantitative assessment of the irreversible character of
the index dynamics. This irreversibility enters as a key ingredient in a novel
simulation strategy of index evolution which demonstrates the predictive
potential of the model.
