Determining Minimum Embedding Dimension in Short Time Series using Precisely Averaged False-nearest-neighbors Approach

A novel method is proposed to determine the minimum embedding dimension on the basis of the false nearest nodes (FNN) and the averaged false neighbors (AFN). We take all the false nearest nodes into account and develop two parameters G₁ and G₂ instead of E₁ and E₂ defined by AFN method for analyzing time series. Several short chaotic time series were tested. The proposed method shows more precise than AFN method and requires less subjective parameters than FNN method. The method is effective even if a time series suffers the corruption with a white Gaussian noise of 20%. It can deal with the experimental chaotic signals from the fiber ring laser based on a semiconductor optical amplifier (SOA), while AFN method fails.