Improved false nearest neighbor method to detect determinism in time series data

The false nearest neighbor method introduced by Kennel et al.. [Phys. Rev. A 45, 3403 (1992)] is revisited and modified in order to ensure a correct distinction between low-dimensional chaotic data and noise. Still, correlated noise processes can yield vanishing percentages of false nearest neighbors for rather low embedding dimensions and can be mistaken for deterministic signals. Therefore, the false nearest neighbors method has always to be combined with a surrogate data test. [S1063-651X(99)08510-4].