Before revision: Financial data give an opportunity to uncover the non-stationarity which may be hidden in many single time-series. Five years of daily Euro/ Dollar trading records in the about three hours following the New York opening session are shown to give an accurate ensemble representation of the self-similar ,
After revision: A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such a model must be compared with the data of a single process realization in our records. In order to give statistical significance to such a comparison, assumptions of stationarity for some quantities extracted from the single historical time series, like the distribution of the returns over a given time interval, cannot be avoided. Such assumptions entail the risk of masking or misrepresenting non-stationarities of the underlying process, and of giving an incorrect account of its correlations. Here we overcome this difficulty by showing that five years of daily Euro/ Dollar trading records in the about three hours following the New York opening session are shown to give an accurate ensemble representation of the self-similar ,