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Modeling dependence via copula of functionals of Fourier coefficients

Author

Listed:
  • Charles Fontaine

    (King Abdullah University of Science and Technology (KAUST)
    Université de Paris-Nanterre)

  • Ron D. Frostig

    (University of California-Irvine)

  • Hernando Ombao

    (King Abdullah University of Science and Technology (KAUST))

Abstract

The goal of this paper is to develop a measure for characterizing complex dependence between time series that cannot be captured by traditional measures such as correlation and coherence. Our approach is to use copula models of functionals of the Fourier coefficients which is a generalization of coherence. Here, we use standard parametric copula models with a single parameter from both elliptical and Archimedean families. Our approach is to analyze changes in activity in local field potentials in the rat cortex prior to and immediately following the onset of stroke. We present the necessary theoretical background, the multivariate models and an illustration of our methodology on these local field potential data. Simulations with nonlinear dependent data reveal that there is information that is missed by not taking into account dependence on specific frequencies. Moreover, these simulations demonstrate how our proposed method captures more complex nonlinear dependence between time series. Finally, we illustrate our copula-based approach in the analysis of local field potentials of rats.

Suggested Citation

  • Charles Fontaine & Ron D. Frostig & Hernando Ombao, 2020. "Modeling dependence via copula of functionals of Fourier coefficients," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1125-1144, December.
  • Handle: RePEc:spr:testjl:v:29:y:2020:i:4:d:10.1007_s11749-020-00703-5
    DOI: 10.1007/s11749-020-00703-5
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    References listed on IDEAS

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    1. Mark Fiecas & Hernando Ombao, 2016. "Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1440-1453, October.
    2. Giovanni Motta & Hernando Ombao, 2012. "Evolutionary Factor Analysis of Replicated Time Series," Biometrics, The International Biometric Society, vol. 68(3), pages 825-836, September.
    3. Kjersti Aas & Daniel Berg, 2009. "Models for construction of multivariate dependence - a comparison study," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 639-659.
    4. Rustam Ibragimov, 2005. "Copula-Based Dependence Characterizations and Modeling for Time Series," Harvard Institute of Economic Research Working Papers 2094, Harvard - Institute of Economic Research.
    5. Freyermuth, Jean-Marc & Ombao, Hernando & von Sachs, Rainer, 2010. "Tree-Structured Wavelet Estimation in a Mixed Effects Model for Spectra of Replicated Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 634-646.
    6. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 317-332, September.
    7. Freyermuth, Jean-Marc & Ombao, Hernando & von Sachs, Rainer, 2010. "Tree-structured wavelet estimation in a mixed effects model for Spectra of replicated time series," LIDAM Reprints ISBA 2010020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    9. Ombao, Hernando & von Sachs, Rainer & Guo, Wensheng, 2005. "SLEX Analysis of Multivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 519-531, June.
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    Cited by:

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    2. Farid El Ktaibi & Rachid Bentoumi & Mhamed Mesfioui, 2024. "On the Ratio-Type Family of Copulas," Mathematics, MDPI, vol. 12(11), pages 1-17, June.

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