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Correlation Integral for Stationary Gaussian Time Series

Author

Listed:
  • Jonathan Acosta

    (Pontificia Universidad Católica de Chile)

  • Ronny Vallejos

    (Universidad Técnica Federico Santa María)

  • John Gómez

    (Universidad Técnica Federico Santa María)

Abstract

The correlation integral of a time series is a normalized coefficient that represents the number of close pairs of points of the series lying in phase space. It has been widely studied in a number of disciplines such as phisycs, mechanical engineering, bioengineering, among others, allowing the estimation of the dimension of an attractor in a chaotic regimen. The computation of the dimension of an attractor allows to distinguish deterministic behavior in stochastic processes with a weak structure on the noise. In this paper, we establish a power law for the limiting expected value of the correlation integral for Gaussian stationary time series. Examples with linear and nonlinear time series are used to illustrate the result.

Suggested Citation

  • Jonathan Acosta & Ronny Vallejos & John Gómez, 2024. "Correlation Integral for Stationary Gaussian Time Series," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 191-214, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00318-6
    DOI: 10.1007/s13171-023-00318-6
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