Time series prediction using Lyapunov exponents in embedding phase space

Abstract

A chaotic time series prediction method is proposed. This method is based on the fundament characteristic of chaotic behaviour of sensitive dependence upon initial conditions (SDUIC) and Lyapunov exponents (LE) is a measure of the SDUIC in chaotic systems. Because LE of chaotic time series data provide a quantitative analysis of system dynamics in different embedding dimension after embedding a chaotic time series in different embedding dimension phase spaces, a multi-dimension chaotic time series prediction using LE is proposed. This is done by first reconstructing a phase space using chaotic time series and then using LE as quantitative parameters to predict unknown phase space points, then transferring the phase space points to the time domain, and we can get the predicted chaotic time series data. We analyse the fundament characteristics of chaotic time series and LE, and deduce the proposed method. A computer simulation is carried out. The results of the simulation show that the proposed method is simple, practical and effective.