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

physical review. e, statistical, nonlinear and soft matter physics

Random cascade model in the limit of infinite integral scale as the  exponential of a non-stationary $1/f$ noise. Application to volatility  fluctuations in stock markets