Introduction of higher order statistics for estimating the dimension of chaotic time series

Given an irregular time series, an important issue is to determine whether it stems from a stochastic or a chaotic (i.e. deterministic with few degrees of freedom) system. This is generally achieved by studying the geometry of a reconstructed attractor, although it is known that some purely stochastic processes can be associated with low-dimension attractors. It is shown that an effective estimation of the number of degrees of freedom can be obtained better through a (local) independent component analysis.<>