RT Journal Article
T1 Transforming Gaussian correlations. Applications to generating long-range power-law correlated time series with arbitrary distribution
A1 Carpena-Sánchez, Pedro Juan
A1 Bernaola-Galván, Pedro Ángel
A1 Gómez Extremera, Manuel
A1 Coronado-Jiménez, Ana Victoria
K1 Pulso cardíaco - Modelos matemáticos
K1 Procesado de señales
AB The observable outputs of many complex dynamical systems consist in time series exhibitingautocorrelation functions of great diversity of behaviors, including long-range power-law autocorre-lation functions, as a signature of interactions operating at many temporal or spatial scales. Often,numerical algorithms able to generate correlated noises reproducing the properties of real time se-ries are used to study and characterize such systems. Typically, those algorithms produce Gaussiantime series. However, real, experimentally observed time series are often non-Gaussian, and mayfollow distributions with a diversity of behaviors concerning the support, the symmetry or the tailproperties. Given a correlated Gaussian time series, it is always possible to transform it into a timeseries with a different distribution, but the question is how this transformation affects the behaviorof the autocorrelation function. Here, we study analytically and numerically how the Pearson’s cor-relation of two Gaussian variables changes when the variables are transformed to follow a differentdestination distribution. Specifically, we consider bounded and unbounded distributions, symmetricand non-symmetric distributions, and distributions with different tail properties, from decays fasterthan exponential to heavy tail cases including power-laws, and we find how these properties affectthe correlation of the final variables. We extend these results to Gaussian time series which aretransformed to have a different marginal distribution, and show how the autocorrelation function ofthe final non-Gaussian time series depends on the Gaussian correlations and on the final marginaldistribution.
PB American Institute of Physics
YR 2020
FD 2020-08-21
LK https://hdl.handle.net/10630/29925
UL https://hdl.handle.net/10630/29925
LA eng
NO Política de acceso abierto tomada de: https://v2.sherpa.ac.uk/id/publication/9866?template=romeo
NO Consejerı́a de Conocimiento, Investigación y Universidad, Junta de Andalucía and European Regional Development Fund (ERDF), ref. SOMM17/6105/UGR and FQM-362.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026