Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay [Formula: see text] and embedding dimension p for phase space reconstruction. The value of [Formula: see text] can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that [Formula: see text] should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay [Formula: see text] , which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally [Formula: see text] and [Formula: see text]. In this paper, we suggest a simple method for estimating [Formula: see text] and [Formula: see text] based on symbolic analysis and symbolic entropy. As in the C-C method, [Formula: see text] is estimated as the first local optimal time delay and [Formula: see text] as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes