Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-rea...
| Autores: | , , , , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/144084 |
| Acesso em linha: | http://hdl.handle.net/11336/144084 |
| Access Level: | acceso abierto |
| Palavra-chave: | CHAOTIC OSCILLATOR COMPLEXITY DYNAMICAL SYSTEM HÖLDER EXPONENTS MULTIFRACTAL ANALYSIS MULTIFRACTAL SPECTRUM SINGULARITY TIME-SERIES ANALYSIS https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| Resumo: | The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-realized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of Hölder exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality. |
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