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A matrix approach to get the variance of the square of the fluctuation function of the DFA

hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
dc.contributor.authorGRIVEL, Eric
hal.structure.identifierTHALES Avionics Electrical Systems [TAES]
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorBERTHELOT, Bastien
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierUniversité de Bordeaux [UB]
dc.contributor.authorLEGRAND, Pierrick
dc.date.accessioned2024-04-04T02:31:30Z
dc.date.available2024-04-04T02:31:30Z
dc.date.created2021
dc.date.issued2021
dc.identifier.issn1051-2004
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190314
dc.description.abstractEnThe fluctuation analysis (FA) and the detrended fluctuation analysis (DFA) make it possible to estimate the Hurst exponent H, which characterizes the self-similarity of a signal. Both are based on the fact that the so-called fluctuation function, which can be seen as an approximation of the standard deviation of the process scaled in time by multiplying the time variable by a positive constant, depends on H. The main novelty of the paper is to provide the expression of the variance of the square of the fluctuation function, by using a matrix formulation. We show that it depends on the correlation function of the signal under study when it is zero-mean and Gaussian. Illustrations are given when dealing with a zero-mean white Gaussian noise. Moving average processes and first-order autoregressive processes are also addressed.
dc.language.isoen
dc.publisherElsevier
dc.rights.urihttp://creativecommons.org/licenses/by-nc/
dc.subject.enDFA
dc.subject.enFA
dc.subject.enStatistical analysis
dc.subject.enVariance
dc.title.enA matrix approach to get the variance of the square of the fluctuation function of the DFA
dc.typeArticle de revue
dc.identifier.doi10.1016/j.dsp.2021.103346
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
bordeaux.journalDigital Signal Processing
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03456525
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03456525v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Digital%20Signal%20Processing&rft.date=2021&rft.eissn=1051-2004&rft.issn=1051-2004&rft.au=GRIVEL,%20Eric&BERTHELOT,%20Bastien&LEGRAND,%20Pierrick&rft.genre=article


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