A matrix approach to get the variance of the square of the fluctuation function of the DFA
| dc.rights.license | open | en_US |
| hal.structure.identifier | Laboratoire de l'intégration, du matériau au système [IMS] | |
| dc.contributor.author | GRIVEL, Eric | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BERTHELOT, Bastien | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LEGRAND, Pierrick
IDREF: 094614032 | |
| dc.date.accessioned | 2022-07-13T12:20:15Z | |
| dc.date.available | 2022-07-13T12:20:15Z | |
| dc.date.created | 2021 | |
| dc.date.issued | 2022-04-15 | |
| dc.identifier.issn | 1051-2004 | en_US |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/140476 | |
| dc.description.abstractEn | The 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.iso | EN | en_US |
| dc.subject.en | DFA | |
| dc.subject.en | FA | |
| dc.subject.en | Statistical analysis | |
| dc.subject.en | Variance | |
| dc.title.en | A matrix approach to get the variance of the square of the fluctuation function of the DFA | |
| dc.type | Article de revue | en_US |
| dc.identifier.doi | 10.1016/j.dsp.2021.103346 | en_US |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | en_US |
| bordeaux.journal | Digital Signal Processing | en_US |
| bordeaux.volume | 122 | |
| bordeaux.hal.laboratories | Laboratoire d’Intégration du Matériau au Système (IMS) - UMR 5218 | en_US |
| bordeaux.institution | Université de Bordeaux | en_US |
| bordeaux.institution | Bordeaux INP | en_US |
| bordeaux.institution | CNRS | en_US |
| bordeaux.peerReviewed | oui | en_US |
| bordeaux.inpress | non | en_US |
| bordeaux.import.source | hal | |
| hal.identifier | hal-03456525 | |
| hal.version | 1 | |
| hal.export | false | |
| workflow.import.source | hal | |
| dc.rights.cc | Pas de Licence CC | en_US |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Digital%20Signal%20Processing&rft.date=2022-04-15&rft.volume=122&rft.eissn=1051-2004&rft.issn=1051-2004&rft.au=GRIVEL,%20Eric&BERTHELOT,%20Bastien&LEGRAND,%20Pierrick&rft.genre=article |
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