Levels of complexity in financial markets

We consider different levels of complexity which are observed in the empiri cal investigation of financial time series. We discuss recent empirical and theoretical work showing that statistical properties of financial time ser ies are rather complex under several ways. Specifically, they are complex w ith respect to their (i) temporal and (ii) ensemble properties. Moreover, t he ensemble return properties show a behavior which is specific to the natu re of the trading day reflecting if it is a normal or an extreme trading da y. (C) 2001 Elsevier Science B.V. All rights reserved.