ABSTRACT
Discrete time series can represent the occurrences of either a deterministic or a random process. A basic problem when dealing with discrete time series is to ascertain whether the series is produced by a deterministic or stochastic system. Dynamical system theory provides powerful techniques to assess whether a set of equations (in a suitable embedding space) underlies the dynamics. In this case the trajectory can be predicted whenever the initial conditions are known with absolute precision. On the contrary, a stochastic system is characterised by a complete unpredictability of the trajectories. In order to keep control of the divergence of the corresponding trajectories, it is essential to take a reasonable low value of the iteration parameter, since in a deterministic chaotic system the trajectories diverge exponentially. The computation of Lyapunov exponents quantifies the divergence of nearby trajectories, providing an analysis of the structure of the attractor.
