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Calculating Embedding Dimension with Confidence Estimates

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Book cover Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.

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Author information

Authors and Affiliations

  1. US Naval Research Lab, Code 6392, Washington, DC, MD, 20375, USA

    T. L. Carroll

  2. US Naval Research Lab, Code 6395, Washington, DC, MD, 20375, USA

    J. M. Byers

Authors
  1. T. L. Carroll
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  2. J. M. Byers
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Corresponding author

Correspondence to T. L. Carroll .

Editor information

Editors and Affiliations

  1. Space and Naval Warfare Systems Center, San Diego, CA, USA

    Visarath In

  2. Space and Naval Warfare Systems Center, San Diego, CA, USA

    Patrick Longhini

  3. Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA

    Antonio Palacios

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Carroll, T.L., Byers, J.M. (2019). Calculating Embedding Dimension with Confidence Estimates. In: In, V., Longhini, P., Palacios, A. (eds) Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-10892-2_21

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  • DOI: https://doi.org/10.1007/978-3-030-10892-2_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10891-5

  • Online ISBN: 978-3-030-10892-2

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