# Probabilistic analysis of recurrence plots generated by fractional Gaussian noise

1 IDH - Interactive Digital Humans
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Recurrence plots of time series generated by discrete fractional Gaussian noise (fGn) processes are analyzed. We compute the probabilities of occurrence of consecutive recurrence points forming diagonals and verticals in the recurrence plot constructed without embedding. We focus on two recurrence quantification analysis measures related to these lines, respectively, the percent determinism and the laminarity (LAM). The behavior of these two measures as a function of the fGn’s Hurst exponent $H$ is investigated. We show that the dependence of the laminarity with respect to $H$ is monotonic in contrast to the percent determinism. We also show that the length of the diagonal and vertical lines involved in the computation of percent determinism and laminarity has an influence on their dependence on $H$. Statistical tests performed on the $LAM$ measure support its utility to discriminate fGn processes with respect to their $H$ values. These results demonstrate that recurrence plots are suitable for the extraction of quantitative information on the correlation structure of these widespread stochastic processes.
Document type :
Journal articles

Cited literature [31 references]

https://hal-lirmm.ccsd.cnrs.fr/lirmm-02050628
Contributor : Sofiane Ramdani <>
Submitted on : Wednesday, May 22, 2019 - 12:23:36 PM
Last modification on : Wednesday, July 22, 2020 - 3:20:07 AM

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### Citation

Sofiane Ramdani, Frédéric Bouchara, Annick Lesne. Probabilistic analysis of recurrence plots generated by fractional Gaussian noise. Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2018, 28 (8), pp.#085721. ⟨10.1063/1.5030522⟩. ⟨lirmm-02050628⟩

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