Dynamical Systems Perspective and Embedding

The analysis of experimental time series for prediction based on a dynamical systems approach remains a challenging problem. A scalar time series x(t) ∈ ℜ can be considered to be a single component of a many-dimensional process of unknown dimension. In this chapter we adopt the working hypothesis that many classes of experimental time series may be analysed within the framework of a dynamical systems approach. We are assuming that the state of a system is given by a point 5 evolving in a multidimensional state space Γ. Then the motion of s in Γ characterises the dynamics of the system.