Selection of embedding parameters for nonlinear models: Application to physiological time series data

ABSRACT The usual approach to nonlinear time series modeling consists of two steps: reconstruct the topological structure of the dynamics (with a time delay embedding), and perform some surface fitting to estimate the evolution operator. We show that the usual method of estimating time delay and embedding dimension is sub-optimal when one is concerned with modeling the dynamics. We introduce an algorithmic method for choosing the optimal embedding strategy and show that this provides improved modeling results for experimental time series of human infant respiratory effort and arrhythmic human electrocardiogram recordings.