Stock market dynamics

We elucidate on several empirical statistical observations of stock market returns. Moreover, we find that these properties are recurrent and are also present in invariant measures of low-dimensional dynamical systems. Thus, we propose that the returns are modeled by the first Poincaré return time of a low-dimensional chaotic trajectory. This modeling, which captures the recurrent properties of the return fluctuations, is able to predict well the evolution of the observed statistical quantities. In addition, it explains the reason for which stocks present simultaneously dynamical properties and high uncertainties. In our analysis, we use data from the S&P 500 index and the Brazilian stock Telebrás.