Modeling non-stationarities in high-frequency financial time series

We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We find that non-stationarities detected in other markets in the past are still there. Moreover, scaling properties reported in the previous literature for other high-frequency financial data are approximately valid as well. Finally, we propose a simple method for describing non-stationary returns, based on a non-homogeneous normal compound Poisson process and we test this model against the empirical findings. It turns out that the model can reproduce several stylized facts of high-frequency financial time series.