Biases in the Simulation and Analysis of Fractal Processes
Joint Authors
Delignières, Didier
Roume, Clément
Ezzina, Samar
Blain, Hubert
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-12-03
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Fractal processes have recently received a growing interest, especially in the domain of rehabilitation.
More precisely, the evolution of fractality with aging and disease, suggesting a loss of complexity, has inspired a number of studies that tried, for example, to entrain patients with fractal rhythms.
This kind of study requires relevant methods for generating fractal signals and for assessing the fractality of the series produced by participants.
In the present work, we engaged a cross validation of three methods of generation and three methods of analysis.
We generated exact fractal series with the Davies–Harte (DH) algorithm, the spectral synthesis method (SSM), and the ARFIMA simulation method.
The series were analyzed by detrended fluctuation analysis (DFA), power spectral density (PSD) method, and ARFIMA modeling.
Results show that some methods of generation present systematic biases: DH presented a strong bias toward white noise in fBm series close to the 1/f boundary and SSM produced series with a larger variability around the expected exponent, as compared with other methods.
In contrast, ARFIMA simulations provided quite accurate series, without major bias.
Concerning the methods of analysis, DFA tended to systematically underestimate fBm series.
In contrast, PSD yielded overestimates for fBm series.
With DFA, the variability of estimates tended to increase for fGn series as they approached the 1/f boundary and reached unacceptable levels for fBm series.
The highest levels of variability were produced by PSD.
Finally, ARFIMA methods generated the best series and provided the most accurate and less variable estimates.
American Psychological Association (APA)
Roume, Clément& Ezzina, Samar& Blain, Hubert& Delignières, Didier. 2019. Biases in the Simulation and Analysis of Fractal Processes. Computational and Mathematical Methods in Medicine،Vol. 2019, no. 2019, pp.1-12.
https://search.emarefa.net/detail/BIM-1130552
Modern Language Association (MLA)
Roume, Clément…[et al.]. Biases in the Simulation and Analysis of Fractal Processes. Computational and Mathematical Methods in Medicine No. 2019 (2019), pp.1-12.
https://search.emarefa.net/detail/BIM-1130552
American Medical Association (AMA)
Roume, Clément& Ezzina, Samar& Blain, Hubert& Delignières, Didier. Biases in the Simulation and Analysis of Fractal Processes. Computational and Mathematical Methods in Medicine. 2019. Vol. 2019, no. 2019, pp.1-12.
https://search.emarefa.net/detail/BIM-1130552
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1130552