Correlation Integral for Stationary Gaussian Time Series

Jonathan Acosta (), Ronny Vallejos () and John Gómez ()
Additional contact information
Jonathan Acosta: Pontificia Universidad Católica de Chile
Ronny Vallejos: Universidad Técnica Federico Santa María
John Gómez: Universidad Técnica Federico Santa María

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 7, 214 pages

Abstract: 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.

Keywords: Correlation integral; Stationary time series; Gaussian process; Power law; Nonlinear time series; 62M10; 62H20; 60G10 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13171-023-00318-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00318-6

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-023-00318-6

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().