A novel approach for estimation of optimal embedding parameters of nonlinear time series by structural learning of neural network

Abstract

In this work a novel approach for estimation of embedding parameters for reconstruction of underlying dynamical system from the observed nonlinear time series by a feedforward neural network with structural learning is proposed. The proposed scheme of optimal estimation of embedding parameters can be viewed as a global non-uniform embedding. It has been found that the proposed method is more efficient for estimating embedding parameters for reconstruction of the attractor in the phase space than conventional uniform embedding methods. The simulation has been done with Henon series and three other real benchmark data sets. The simulation results for short term prediction of Henon Series and the bench mark time series with the estimated embedding parameters also show that the estimated parameters with proposed technique are better than the estimated parameters with the conventional method in terms of the prediction accuracy. The proposed technique seems to be an efficient candidate for prediction of future values of noisy real world time series.