Methodology of estimating the embedding dimension in chaos time series based on the prediction performance of K-CV_GRNN

Abstract

This paper is about the methodology of estimating the embedding dimension for phase space reconstruction of chaotic time series according to the Takens theorem. Based on the prediction of nonlinear performance, it proposed an approach to the estimation of the embedding dimension based on the Generalized Regression Neural Network of K-Fold Cross Validation to solve the problems of small data, existing noise, subjective evaluation indexes in the prediction of chaotic time series. That is, it determines the embedding dimension by considering the variation (prediction accuracy and normalized variance) of the performance of prediction model of chaotic time series with embedding dimension. Numerical simulations verify that the method is applicable for determining an appropriate embedding dimension.