arXiv:cond-mat/0308064v1 5 Aug 2003 Dynamical model and nonextensive statistical mechanics of a market index on large time windows M. Ausloos 1 and K. Ivanova 2 1 GRASP and SUPRAS, B5, Sart Tilman, B-4000 Li` ege, Belgium 2 Pennsylvania State University, University Park, PA 16802, USA February 2, 2008 Abstract The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonexten- sive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the in- termittent behavior of turbulent flows describes the behavior of nor- malized log-returns for such a financial market index, for small and large time windows, both for small and large log-returns. These turbu- lent market volatility (of normalized log-returns) distributions can be sufficiently well fitted with a χ 2 -distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at ca. a 200 day time lag. The intermittency exponent (κ) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, -thereby giving weight to the model. The large value of κ points to a large number of cascades in the turbulent process. The first Kramers-Moyal coeffi- cient in the Fokker-Planck equation is almost equal to zero, indicating 1