Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data

Autores
Von Wegner, Frederic; Laufs, Helmut; Tagliazucchi, Enzo Rodolfo
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Long-range memory in time series is often quantified by the Hurst exponent H, a measure of the signal's variance across several time scales. We analyze neurophysiological time series from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state experiments with two standard Hurst exponent estimators and with the time-lagged mutual information function applied to discretized versions of the signals. A confidence interval for the mutual information function is obtained from surrogate Markov processes with equilibrium distribution and transition matrix identical to the underlying signal. For EEG signals, we construct an additional mutual information confidence interval from a short-range correlated, tenth-order autoregressive model. We reproduce the previously described Hurst phenomenon (H>0.5) in the analytical amplitude of alpha frequency band oscillations, in EEG microstate sequences, and in fMRI signals, but we show that the Hurst phenomenon occurs without long-range memory in the information-theoretical sense. We find that the mutual information function of neurophysiological data behaves differently from fractional Gaussian noise (fGn), for which the Hurst phenomenon is a sufficient condition to prove long-range memory. Two other well-characterized, short-range correlated stochastic processes (Ornstein-Uhlenbeck, Cox-Ingersoll-Ross) also yield H>0.5, whereas their mutual information functions lie within the Markovian confidence intervals, similar to neural signals. In these processes, which do not have long-range memory by construction, a spurious Hurst phenomenon occurs due to slow relaxation times and heteroscedasticity (time-varying conditional variance). In summary, we find that mutual information correctly distinguishes long-range from short-range dependence in the theoretical and experimental cases discussed. Our results also suggest that the stationary fGn process is not sufficient to describe neural data, which seem to belong to a more general class of stochastic processes, in which multiscale variance effects produce Hurst phenomena without long-range dependence. In our experimental data, the Hurst phenomenon and long-range memory appear as different system properties that should be estimated and interpreted independently.
Fil: Von Wegner, Frederic. Goethe Universitat Frankfurt; Alemania
Fil: Laufs, Helmut. University Hospital Kiel; Alemania. Goethe Universitat Frankfurt; Alemania
Fil: Tagliazucchi, Enzo Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Goethe Universitat Frankfurt; Alemania
Materia
HURST EXPONENT
LONG RANGE CORRELATIONS
EEG
MICROSTATES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/98594

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network_name_str CONICET Digital (CONICET)
spelling Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI dataVon Wegner, FredericLaufs, HelmutTagliazucchi, Enzo RodolfoHURST EXPONENTLONG RANGE CORRELATIONSEEGMICROSTATEShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.6https://purl.org/becyt/ford/1Long-range memory in time series is often quantified by the Hurst exponent H, a measure of the signal's variance across several time scales. We analyze neurophysiological time series from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state experiments with two standard Hurst exponent estimators and with the time-lagged mutual information function applied to discretized versions of the signals. A confidence interval for the mutual information function is obtained from surrogate Markov processes with equilibrium distribution and transition matrix identical to the underlying signal. For EEG signals, we construct an additional mutual information confidence interval from a short-range correlated, tenth-order autoregressive model. We reproduce the previously described Hurst phenomenon (H>0.5) in the analytical amplitude of alpha frequency band oscillations, in EEG microstate sequences, and in fMRI signals, but we show that the Hurst phenomenon occurs without long-range memory in the information-theoretical sense. We find that the mutual information function of neurophysiological data behaves differently from fractional Gaussian noise (fGn), for which the Hurst phenomenon is a sufficient condition to prove long-range memory. Two other well-characterized, short-range correlated stochastic processes (Ornstein-Uhlenbeck, Cox-Ingersoll-Ross) also yield H>0.5, whereas their mutual information functions lie within the Markovian confidence intervals, similar to neural signals. In these processes, which do not have long-range memory by construction, a spurious Hurst phenomenon occurs due to slow relaxation times and heteroscedasticity (time-varying conditional variance). In summary, we find that mutual information correctly distinguishes long-range from short-range dependence in the theoretical and experimental cases discussed. Our results also suggest that the stationary fGn process is not sufficient to describe neural data, which seem to belong to a more general class of stochastic processes, in which multiscale variance effects produce Hurst phenomena without long-range dependence. In our experimental data, the Hurst phenomenon and long-range memory appear as different system properties that should be estimated and interpreted independently.Fil: Von Wegner, Frederic. Goethe Universitat Frankfurt; AlemaniaFil: Laufs, Helmut. University Hospital Kiel; Alemania. Goethe Universitat Frankfurt; AlemaniaFil: Tagliazucchi, Enzo Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Goethe Universitat Frankfurt; AlemaniaAmerican Physical Society2018-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98594Von Wegner, Frederic; Laufs, Helmut; Tagliazucchi, Enzo Rodolfo; Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data; American Physical Society; Physical Review E; 97; 2; 2-2018; 1-52470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.97.022415info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:56:15Zoai:ri.conicet.gov.ar:11336/98594instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:56:15.992CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data
title Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data
spellingShingle Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data
Von Wegner, Frederic
HURST EXPONENT
LONG RANGE CORRELATIONS
EEG
MICROSTATES
title_short Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data
title_full Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data
title_fullStr Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data
title_full_unstemmed Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data
title_sort Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data
dc.creator.none.fl_str_mv Von Wegner, Frederic
Laufs, Helmut
Tagliazucchi, Enzo Rodolfo
author Von Wegner, Frederic
author_facet Von Wegner, Frederic
Laufs, Helmut
Tagliazucchi, Enzo Rodolfo
author_role author
author2 Laufs, Helmut
Tagliazucchi, Enzo Rodolfo
author2_role author
author
dc.subject.none.fl_str_mv HURST EXPONENT
LONG RANGE CORRELATIONS
EEG
MICROSTATES
topic HURST EXPONENT
LONG RANGE CORRELATIONS
EEG
MICROSTATES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.6
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Long-range memory in time series is often quantified by the Hurst exponent H, a measure of the signal's variance across several time scales. We analyze neurophysiological time series from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state experiments with two standard Hurst exponent estimators and with the time-lagged mutual information function applied to discretized versions of the signals. A confidence interval for the mutual information function is obtained from surrogate Markov processes with equilibrium distribution and transition matrix identical to the underlying signal. For EEG signals, we construct an additional mutual information confidence interval from a short-range correlated, tenth-order autoregressive model. We reproduce the previously described Hurst phenomenon (H>0.5) in the analytical amplitude of alpha frequency band oscillations, in EEG microstate sequences, and in fMRI signals, but we show that the Hurst phenomenon occurs without long-range memory in the information-theoretical sense. We find that the mutual information function of neurophysiological data behaves differently from fractional Gaussian noise (fGn), for which the Hurst phenomenon is a sufficient condition to prove long-range memory. Two other well-characterized, short-range correlated stochastic processes (Ornstein-Uhlenbeck, Cox-Ingersoll-Ross) also yield H>0.5, whereas their mutual information functions lie within the Markovian confidence intervals, similar to neural signals. In these processes, which do not have long-range memory by construction, a spurious Hurst phenomenon occurs due to slow relaxation times and heteroscedasticity (time-varying conditional variance). In summary, we find that mutual information correctly distinguishes long-range from short-range dependence in the theoretical and experimental cases discussed. Our results also suggest that the stationary fGn process is not sufficient to describe neural data, which seem to belong to a more general class of stochastic processes, in which multiscale variance effects produce Hurst phenomena without long-range dependence. In our experimental data, the Hurst phenomenon and long-range memory appear as different system properties that should be estimated and interpreted independently.
Fil: Von Wegner, Frederic. Goethe Universitat Frankfurt; Alemania
Fil: Laufs, Helmut. University Hospital Kiel; Alemania. Goethe Universitat Frankfurt; Alemania
Fil: Tagliazucchi, Enzo Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Goethe Universitat Frankfurt; Alemania
description Long-range memory in time series is often quantified by the Hurst exponent H, a measure of the signal's variance across several time scales. We analyze neurophysiological time series from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state experiments with two standard Hurst exponent estimators and with the time-lagged mutual information function applied to discretized versions of the signals. A confidence interval for the mutual information function is obtained from surrogate Markov processes with equilibrium distribution and transition matrix identical to the underlying signal. For EEG signals, we construct an additional mutual information confidence interval from a short-range correlated, tenth-order autoregressive model. We reproduce the previously described Hurst phenomenon (H>0.5) in the analytical amplitude of alpha frequency band oscillations, in EEG microstate sequences, and in fMRI signals, but we show that the Hurst phenomenon occurs without long-range memory in the information-theoretical sense. We find that the mutual information function of neurophysiological data behaves differently from fractional Gaussian noise (fGn), for which the Hurst phenomenon is a sufficient condition to prove long-range memory. Two other well-characterized, short-range correlated stochastic processes (Ornstein-Uhlenbeck, Cox-Ingersoll-Ross) also yield H>0.5, whereas their mutual information functions lie within the Markovian confidence intervals, similar to neural signals. In these processes, which do not have long-range memory by construction, a spurious Hurst phenomenon occurs due to slow relaxation times and heteroscedasticity (time-varying conditional variance). In summary, we find that mutual information correctly distinguishes long-range from short-range dependence in the theoretical and experimental cases discussed. Our results also suggest that the stationary fGn process is not sufficient to describe neural data, which seem to belong to a more general class of stochastic processes, in which multiscale variance effects produce Hurst phenomena without long-range dependence. In our experimental data, the Hurst phenomenon and long-range memory appear as different system properties that should be estimated and interpreted independently.
publishDate 2018
dc.date.none.fl_str_mv 2018-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/98594
Von Wegner, Frederic; Laufs, Helmut; Tagliazucchi, Enzo Rodolfo; Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data; American Physical Society; Physical Review E; 97; 2; 2-2018; 1-5
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98594
identifier_str_mv Von Wegner, Frederic; Laufs, Helmut; Tagliazucchi, Enzo Rodolfo; Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data; American Physical Society; Physical Review E; 97; 2; 2-2018; 1-5
2470-0053
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.97.022415
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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