Estimating the Embedding Dimension Distribution of Time Series with SOMOS

The paper proposes a new method to estimate the distribution of the embedding dimension associated with a time series, using the Self Organizing Map decision taken in Output Space (SOMOS) dimensionality reduction neural network. It is shown that SOMOS, besides estimating the embedding dimension, it also provides an approximation of the overall distribution of such dimension for the set where the time series evolves. Such estimation can be employed to select a proper window size in different predictor schemes; also, it can provide a measure of the future predictability at a given instant of time. The results are illustrated via the analysis of time series generated from both chaotic Hénon map and Lorenz system.