Application of methods based on higher-order statistics for chaotic time series analysis

The aim of this paper is to illustrate some applications of HOS within the context of chaotic time series analysis. After reviewing briefly some of the most popular methods and approaches used in chaotic signal analysis, we show how HOS may lead to some significant improvement. First, an HOS expansion of the mutual information is shown to provide an easy way to estimate the reconstruction delay that must be used in the embedding reconstruction method. Then, a fourth-order extension of the local intrinsic dimension analysis (LID) is proposed. The ability of this HOS extension to separate between chaotic and stochastic behaviour is illustrated by examples on simulated data and experimental time series.