IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v86y2024i1d10.1007_s13171-023-00318-6.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-023-00318-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-023-00318-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kugiumtzis, Dimitris & Tsimpiris, Alkiviadis, 2010. "Measures of Analysis of Time Series (MATS): A MATLAB Toolkit for Computation of Multiple Measures on Time Series Data Bases," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i05).
    2. C. A. Glasbey, 2001. "Non‐linear autoregressive time series with multivariate Gaussian mixtures as marginal distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 143-154.
    3. Yolanda Caballero & Ramón Giraldo & Jorge Mateu, 2022. "A spatial randomness test based on the box-counting dimension," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(3), pages 499-524, September.
    4. Lahmiri, Salim & Tadj, Chakib & Gargour, Christian & Bekiros, Stelios, 2021. "Characterization of infant healthy and pathological cry signals in cepstrum domain based on approximate entropy and correlation dimension," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lahmiri, Salim & Tadj, Chakib & Gargour, Christian & Bekiros, Stelios, 2022. "Deep learning systems for automatic diagnosis of infant cry signals," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. Patrick, Joshua D. & Harvill, Jane L. & Hansen, Clifford W., 2016. "A semiparametric spatio-temporal model for solar irradiance data," Renewable Energy, Elsevier, vol. 87(P1), pages 15-30.
    3. Kostić, Srđan & Vasović, Nebojša & Perc, Matjaž & Toljić, Marinko & Nikolić, Dobrica, 2013. "Stochastic nature of earthquake ground motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4134-4145.
    4. Ioulia Papageorgiou, 2016. "Sampling from Correlated Populations: Optimal Strategies and Comparison Study," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 119-151, May.
    5. Varin, Cristiano & Vidoni, Paolo, 2006. "Pairwise likelihood inference for ordinal categorical time series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2365-2373, December.
    6. Kalliovirta, Leena & Meitz, Mika & Saikkonen, Pentti, 2016. "Gaussian mixture vector autoregression," Journal of Econometrics, Elsevier, vol. 192(2), pages 485-498.
    7. Chen, Wei-Shing, 2011. "Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1332-1342.
    8. Benbachir, Saâd & El Alaoui, Marwane, 2011. "A Multifractal Detrended Fluctuation Analysis of the Moroccan Stock Exchange," MPRA Paper 49003, University Library of Munich, Germany.
    9. Srđan Kostić & Matjaž Perc & Nebojša Vasović & Slobodan Trajković, 2013. "Predictions of Experimentally Observed Stochastic Ground Vibrations Induced by Blasting," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-13, December.
    10. Lahmiri, Salim & Tadj, Chakib & Gargour, Christian & Bekiros, Stelios, 2023. "Optimal tuning of support vector machines and k-NN algorithm by using Bayesian optimization for newborn cry signal diagnosis based on audio signal processing features," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    11. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    12. Leena Kalliovirta & Mika Meitz & Pentti Saikkonen, 2015. "A Gaussian Mixture Autoregressive Model for Univariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 247-266, March.
    13. Iliopoulos, A.C. & Nikolaidis, N.S. & Aifantis, E.C., 2015. "Portevin–Le Chatelier effect and Tsallis nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 509-518.
    14. Gkarlaouni, Charikleia & Lasocki, Stanislaw & Papadimitriou, Eleftheria & George, Tsaklidis, 2017. "Hurst analysis of seismicity in Corinth rift and Mygdonia graben (Greece)," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 30-42.
    15. Elsa Vazquez & Jeffrey R. Wilson, 2021. "Partitioned method of valid moment marginal model with Bayes interval estimates for correlated binary data with time-dependent covariates," Computational Statistics, Springer, vol. 36(4), pages 2701-2718, December.
    16. Zhou, Shuang & Wang, Xingyuan & Zhou, Wenjie & Zhang, Chuan, 2022. "Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00318-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.