Nonlinear prediction as a way of distinguishing chaos from random fractal sequences

It is shown here that, by determining the scaling properties of the prediction error as a function of time, nonlinear prediction can be used to distinguish between chaos and random fractal sequences. Random fractal sequences are a particular class of colored noise which represent stochastic systems with power-law spectra. The recognition of this type of noise is of practical importance, as measurements from a variety of dynamical systems may over some range of frequencies exhibit power-law spectra.