False nearest neighbors (FNN) is one of the essential methods used in estimating the minimally sufficient embedding dimension in delay coordinate embedding of deterministic time series. Its use for stochastic and noisy deterministic time series is problematic and erroneously indicates a finite embedding dimension. Various modifications to the original method have been proposed to mitigate this problem, but those are still not reliable for noisy time series. Nearest neighbor statistics are studied for uncorrelated random time series and contrasted with the deterministic statistics. A new FNN metric is constructed and its performance is evaluated for deterministic, stochastic, and random time series. The results are also contrasted with surrogate data analysis and show that the new metric is robust to noise. It also clearly identifies random time series as not having a finite embedding dimension and provides information about the deterministic part of stochastic processes. The new metric can also be used for differentiating between chaotic and random time series.
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ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 17–20, 2014
Buffalo, New York, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-4641-4
PROCEEDINGS PAPER
Statistical Characterization of Nearest Neighbors to Reliably Estimate Minimum Embedding Dimension
David Chelidze
David Chelidze
University of Rhode Island, Kingston, RI
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David Chelidze
University of Rhode Island, Kingston, RI
Paper No:
DETC2014-34746, V008T11A015; 10 pages
Published Online:
January 13, 2015
Citation
Chelidze, D. "Statistical Characterization of Nearest Neighbors to Reliably Estimate Minimum Embedding Dimension." Proceedings of the ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8: 26th Conference on Mechanical Vibration and Noise. Buffalo, New York, USA. August 17–20, 2014. V008T11A015. ASME. https://doi.org/10.1115/DETC2014-34746
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