False neighbors and false strands: A reliable minimum embedding dimension algorithm

Abstract

The time-delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer embedding dimension. We demonstrate a reliable method to estimate the minimum necessary embedding dimension that improves upon previous methods by correcting for systematic effects due to temporal oversampling, autocorrelation, and changing time lag. The method gives a sharp and reliable indication of the proper dimension. With little computational cost, the method also distinguish easily between infinite-dimensional colored noise—including noisy periodicity—and low-dimensional dynamics.