We propose a simple stochastic model for time series, which captures some relevant stylized facts of financial indexes. In particular, increments are uncorrelated but dependent; the correlation between their absolute values decays exponentially in time for large distances, but for moderate distances has a power low-like decay. Finally, the distribution of the increments obeys scaling and multiscaling relations that are detected on real time series, but are not satisfied by most available models for financial indexes. We also calibrate the model with data of the DJI, obtaining a remarkable agreement between simulations and real data. This is a joint work with A. Andreoli, F. Caravenna and G. Posta