Definition of the fluctuation function in the detrended fluctuation analysis and its variants

Autor: Bastien Berthelot, Audrey Giremus, Pierrick Legrand, Eric Grivel
Přispěvatelé: THALES Avionics Electrical Systems (TAES), THALES Avionics Electrical Systems, Laboratoire de l'intégration, du matériau au système (IMS), Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Méthodes avancées d’apprentissage statistique et de contrôle (ASTRAL), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Naval Group, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB), THALES [France], Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2021
Předmět:
Zdroj: The European Physical Journal B: Condensed Matter and Complex Systems
The European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2021, 94, ⟨10.1140/epjb/s10051-021-00231-7⟩
The European Physical Journal B: Condensed Matter and Complex Systems, 2021, 94, ⟨10.1140/epjb/s10051-021-00231-7⟩
ISSN: 1434-6036
1434-6028
DOI: 10.1140/epjb/s10051-021-00231-7
Popis: International audience; The detrended fluctuation analysis (DFA) and its variants are popular methods to analyze the self-similarity of a signal. Two steps characterize them: firstly, the trend of the centered integrated signal is estimated and removed. Secondly, the properties of the so-called fluctuation function which is an approximation of the standard deviation of the resulting process is analyzed. However, it appears that the statistical mean was assumed to be equal to zero to obtain it. As there is no guarantee that this assumption is true a priori, this hypothesis is debatable. The purpose of this paper is to propose two alternative definitions of the fluctuation function. Then, we compare all of them based on a matrix formulation and the filter-based interpretation we recently proposed. This analysis will be useful to show that the approach proposed in the original paper remains a good compromise in terms of accuracy and computational cost.
Databáze: OpenAIRE
Externí odkaz: