"Empirical analyses of financial data show that price changes cannot be described by a strict-sense stationary stochastic process, since the standard deviation of price changes, namely the volatility, is time-dependent in real markets. Hence, the form of stationarity that is present in financial markets is at best asymptotic stationarity. By analyzing a sufficiently long time series, the asymptotic pdf of prices changes is obtained. The asympttotic pdf gives the large time statistical properties of the stochastic process."
Mantegna and Stanley (2000)