Method of false nearest neighbors: A cautionary note

Abstract

The method of false nearest neighbors [M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992)] has been proposed for detecting deterministic structure in empirical time series and for estimating the embedding dimension if the series is deterministic. We show that the method can falsely indicate that a stationary random process is deterministic. Remedial modifications of the method are proposed.