  In this paper we propose a new model for volatility fluctuations in financial
time series. This model relies on a non-stationary gaussian process that
exhibits aging behavior. It turns out that its properties, over any finite time
interval, are very close to continuous cascade models. These latter models are
indeed well known to reproduce faithfully the main stylized facts of financial
time series. However, it involve a large scale parameter (the so-called
"integral scale" where the cascade is initiated) that is hard to interpret in
finance. Moreover the empirical value of the integral scale is in general
deeply correlated to the overall length of the sample. This feature is
precisely predicted by our model that turns out, as illustrated on various
examples from daily stock index data, to quantitatively reproduce the empirical
observations.
