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DFA-based abacuses providing the Hurst exponent estimate for short-memory processes

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
hal.structure.identifierInstitut Polytechnique de Bordeaux [Bordeaux INP]
dc.contributor.authorGIREMUS, Audrey
dc.date.accessioned2024-04-04T02:33:58Z
dc.date.available2024-04-04T02:33:58Z
dc.date.created2021
dc.date.issued2021
dc.identifier.issn1051-2004
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190521
dc.description.abstractEnThe detrended fluctuation analysis (DFA) and its higher-order variant make it possible to estimate the Hurst exponent and therefore to quantify the long-range dependence of a random process. These methods are popular and used in a wide range of applications where they have been proven to be discriminative to characterize or classify processes. Nevertheless, in practice, the signal may be short-memory. In addition, depending on the number of samples available, there is no guarantee that these methods provide the true value of the Hurst exponent, leading the user to draw erroneous conclusions on the long-range dependence of the signal under study. In this paper, using a matrix formulation and making no approximation, we first propose to analyze how the DFA and its higher-order variant behave with respect to the number of samples available. Illustrations dealing with short-memory data that can be modeled by a white noise, a moving-average process and a random process whose autocorrelation function exponentially decays are given. Finally, to avoid any wrong conclusions, we propose to derive abacuses linking the value provided by the DFA or its variant with the properties of the signal and the number of samples available.
dc.language.isoen
dc.publisherElsevier
dc.rights.urihttp://creativecommons.org/licenses/by-nc/
dc.subject.enDFA
dc.subject.enHigher-order DFA
dc.subject.enHurst coefficient
dc.subject.enSensitivity
dc.subject.enAbacus
dc.title.enDFA-based abacuses providing the Hurst exponent estimate for short-memory processes
dc.typeArticle de revue
dc.identifier.doi10.1016/j.dsp.2021.103102
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
bordeaux.journalDigital Signal Processing
bordeaux.volume116
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03225784
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03225784v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Digital%20Signal%20Processing&rft.date=2021&rft.volume=116&rft.eissn=1051-2004&rft.issn=1051-2004&rft.au=GRIVEL,%20Eric&BERTHELOT,%20Bastien&LEGRAND,%20Pierrick&GIREMUS,%20Audrey&rft.genre=article


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