Determination of the proper embedding parameters for noisy time series

Abstract

We suggest an algorithm for determining the proper delay time and the minimum embedding dimension for Takens' delay-time embedding procedure. This method resorts to the rate of change of the spatial distribution of points on a reconstructed attractor with respect to the delay time, and can be successfully applied to a noisy time series which is too noisy to be discriminated from a sutructureless noisy time series by means of the correlation integral, and also indicates that the proper delay time depends on the embedding dimension.