  We consider different levels of complexity which are observed in the
empirical investigation of financial time series. We discuss recent empirical
and theoretical work showing that statistical properties of financial time
series are rather complex under several ways. Specifically, they are complex
with respect to their (i) temporal and (ii) ensemble properties. Moreover, the
ensemble return properties show a behavior which is specific to the nature of
the trading day reflecting if it is a normal or an extreme trading day.
