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Dimension from covariance matrices.

T L Carroll1, J M Byers1

  • 1U.S. Naval Research Laboratory, Washington, DC 20375, USA.

Chaos (Woodbury, N.Y.)
|March 3, 2017
PubMed
Summary
This summary is machine-generated.

We developed a new method to estimate the embedding dimension of time series data. This approach provides a statistical measure of validity, enhancing the reliability of dynamical system analysis.

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Area of Science:

  • Dynamical Systems Theory
  • Time Series Analysis
  • Nonlinear Dynamics

Background:

  • Estimating the embedding dimension is crucial for analyzing the behavior of dynamical systems from time series data.
  • Current methods often lack a robust measure of the validity of the dimension estimate.
  • Reliable dimension estimation is fundamental for understanding system properties and making predictions.

Purpose of the Study:

  • To introduce a novel method for estimating the embedding dimension from time series.
  • To provide a statistical estimate of the probability that the calculated dimension is valid.
  • To improve the reliability of dynamical system analysis by incorporating validity assessments.

Main Methods:

  • The algorithm embeds the time series signal.
  • It computes covariance matrices from the embedded signal and compares their eigenvalues to those of a Gaussian random process.
  • A statistical test determines the probability that the observed eigenvalues originate from the Gaussian process.

Main Results:

  • The method provides an estimate of the embedding dimension.
  • Crucially, it also yields a probability indicating the validity of this dimension estimate.
  • This validity estimate is a novel contribution compared to existing algorithms.

Conclusions:

  • The described method offers a statistically grounded approach to embedding dimension estimation.
  • The inclusion of a validity probability enhances the trustworthiness of results in dynamical systems analysis.
  • This technique has the potential to improve the accuracy and interpretability of time series analysis in various scientific fields.