ABSTRACT
Recently, J. Scheinkman and B. Le Baron have analyzed a time series of weekly stock returns from the point of view of nonlinear dynamics. In particular, using the Grassberger-Procaccia algorithm, they found the data to be compatible with a deterministic dynamical system of low dimension perturbed by a moderate amount of noise. This chapter analyses the same time series, and obtain an estimate of Lyapunov exponents, that is, rates of exponential growth of small perturbations to initial conditions. It also analyzes the data for temporal homogeneity by producing a recurrence plot to obtain this plot the weekly returns time series is first used to generate a six-dimensional trajectory by the time-delay method. The recurrence plot, apart form a short exceptional period near the beginning of the time series, appears reasonably uniform. This seems to indicate that there is not much drift–in the more than twenty years studied–for the behavior of weekly returns over a few weeks.
